摘要
耦合体系中远离平衡态的非线性时空动力学行为广泛存在于自然界中，对其研究有助于我们理解自然界中的复杂生化时空自组织行为生成和演化机理。本论文以嫁接了BZ反应催化剂的高分子软物质凝胶为反应-扩散载体，探索了高分子凝胶介质中非线性化学反应发生时，耦合体系整体远离非平衡态条件下的时间和空间上的自组织行为，如凝胶自发的发生类似于自然界中动植物所具有的向光和避光运动、多尺度化学脉冲波和各种复杂时空斑图等。本论文通过实验现象、机理解释和数值模拟方面对钌催化Belousov-Zhabotinsky (BZ)反应凝胶体系（即BZ凝胶）中的复杂时空动力学行为进行系统的分析研究。在具体实验中，首先合成具有双键的钌催化剂，将其与聚合物水凝胶接枝共聚，再与BZ反应耦合作用，得到具有光敏特性的自振荡凝胶反应-扩散系统，凝胶介质中的非线性振荡反应过程耦合扩散过程可以形成丰富的时空动力学行为。聚合物空间网络结构有效消除了对流效应对反应-扩散过程的影响，使我们能够系统而全面地研究耦合体系的时空动力学行为。
首先研究了一维毛细管中的钌催化BZ凝胶耦合BZ反应体系，在单向反应-扩散过程中，随着反应底物的消耗和扩散，所形成的化学脉冲波的传播距离呈现多尺度周期性变化趋势，随着时间的推移，传播模式从简单振荡（周期1，P~1）逐渐过渡到周期2（P~2）、周期4（P~4）和周期8（P~8），再经过一段时间的混沌状态传播模式（Chaos），逐渐演化为周期16（P~(16)）传播模式。在实验中发现溴酸盐调制化学脉冲波时空动力学行为效果显著，随着溴酸盐浓度的增大，化学脉冲波传播形式从继发振荡传播模式（Bursting Wave）开始，逐渐演化为周期1（P~1）,周期2（P~2），周期4（P~4）,周期8（P~8）和周期16（P~(16)），并且当溴酸盐浓度增大到112mM以后，BZ凝胶介质中会呈现脉冲和氧化稳态的混合态（Mixture of Oxidized Steady State and Pulse Waves）。改变其它反应底物浓度实验参数，也能有效调制化学脉冲波多尺度传播动力学行为。同时通过均相对比实验，发现相同实验参数条件下如果没有扩散，均相体系振荡行为是简单振荡，这说明扩散在整个多尺度传播模式中发挥重要作用。另外测试了一维凝胶中不同位置的动力学行为，发现在扩散距离不同的条件下，不同局点动力学行为不同，这也再次验证了振荡体系的扩散与反应的耦合导致的物质浓度梯度分布是一维凝胶介质中多尺度脉冲波产生的根本原因。所以，振荡介质和稳定的浓度梯度这两个特征说明了我们研究的化学脉冲波属于相波，是由稳定的相梯度引起的。通过五变量俄勒冈模型（Five-variable Oregonator Model）数值模拟重现了实验现象特征，验证了相关反应扩散实验机理。通过实验和模拟，为我们理解自然界中多尺度生化物理现象提供了很好的启示，促进了对自然界中生物发育等各种复杂时空结构形成机理的理解的理解，而且在此基础上设计的复杂时空动力学自组织模式也有可能应用于现实中。
另外一方面，光敏性的Ru(bpy)3接枝共聚于聚合物凝胶分子链上形成BZ凝胶，在没有外部刺激的条件下由于催化剂在氧化态和还原态之间周期性的转变，导致凝胶分子链间的亲水和斥水性变化，在控制好交联剂密度的条件下可以表现出凝胶体积的周期性膨胀和收缩行为。而作为BZ反应的催化剂还具有独特的光敏特性，在一定的光照条件下，激发态的Ru(bpy)32+﹡可以发生两种不同的光化学反应过程：分别产生抑制剂（Br-）和活化剂（HBrO2）。这就为我们光控BZ凝胶宏观动力学行为提供了可操作性。不同光效应导致凝胶中化学脉冲波的产生频率产生差异。通过差异性光照，调制凝胶介质中化学脉冲波的频率，使凝胶内部动力学行为受到影响，从而控制凝胶受力平衡，实现凝胶的定向移动。实验发现凝胶的运动方向与凝胶介质中化学脉冲波的频率密切相关，凝胶倾向于化学脉冲波频率高的方向移动。通过均相实验发现了光强增大过程中，BZ振荡频率先增大后减小的规律，利用此规律，分别在光诱导区间和光抑制区间实施差异性光照，最终实现了光敏性BZ凝胶发生类似于自然界中动植物所具有的趋光和避光运动。另外，我们还研究了在不同实验参数条件下二维凝胶介质中的时空动力学行为，发现光照和机械力都能作为有效扰动因素改变耦合体系的复杂自组织动力学行为。通过两变量光敏俄勒冈模型（Two-variable Oregonator Model）数值模拟了光照对BZ反应的影响，数值模拟结果和实验现象符合的很好，这在机理解释上也提供了合理的依据。
本课题通过将光敏性的BZ反应催化剂嫁接于高分子软物质分子链上，巧妙的将BZ反应和软物质有机的耦合在一起，来开展反应-扩散介质中的时空斑图动力学和光控光敏性凝胶定向运动动力学行为研究。建立起了能研究贴近自然界中的复杂耦合体系时空动力学行为载体，通过相关实验和模拟工作为设计智能响应性软物质提供了很好的启示。
Stimuli-responsive soft materials coupling with nonlinear chemical reaction are thesuitable mediums for studying the spatiotemporal dynamics of self-organizing behaviors.The coupling system away from non-equilibrium conditions can show many nonlinearspatio-temporal dynamic phenomenons, such as chemical pulse waves, self-oscillation ofvolume changes and complex patterns. This paper mainly focuses on the experimentalphenomena, mechanism explanation and numerical simulation of the spatio-temporaldynamical behaviors in the ruthenium catalyzed Belousov-Zhabotinsky (BZ) gel system. Inexperiment, the catalyst (Ru(bpy)3) with double bond was graft copolymerized with thepolymer chains. Polymer network structure can effectively eliminate the convection effectduring the reaction-diffusion process. It’s feasible to get the stable spatio-temporaldynamics. We can get this functional gels coupled with BZ reaction and monitored thespatio-temporal dynamical behaviors at different experiment conditions.
We first synthesized the BZ gel in one-dimensional capillary, with one end opened and theother sealed. Once the “dead-end” capillary filled with BZ gel touched with BZ solution.Wave initialized from the open end of the tube traveled a finite distance before dissipating.Remarkably, the propagation distance of successive waves was not constant but ratherexhibited complex patterns: multiple-length-scale propagation modes of chemical pulse wavesstarted with P~1and evolved orderly to P~2, P~4, P~8and P~(16)with [NaBrO3]0increased, and finallypropagated into mixed waves. Our results demonstrated that the concentration of NaBrO3canbe used as control parameter to modulate the bifurcations of period-doublingmultiple-length-scale propagation modes. The spatiotemporal patterns were reproduced by areaction-diffusion model using the5-variable Oregonator model for the BZ kinetics. In thesimulate course, we modulated the period of chemical pulse waves by increasing A0(theconcentration of BrO3-). We can see that there is also an evolution of period-doublingbifurcation phenomena with A0increased, which is in complete agreement with theexperimental results. The propagation modes evolved from simple to complex. Change otherexperimental parameters can also modulate the spatio-temporal dynamics. Our works aretrying to set up a useful model system not only for studying the nonlinear chemical dynamics,but also for understanding the multiple scale behaviors in nature. Such as the growth of plant,nutrients are diffusion-fed from the trunk and branches at multiple levels.
On the other hand, the catalyst (Ru(bpy)3) grafted to the polymer molecular chains hasunique photosensitive characteristic. We further investigated the dynamic behavior ofhydrogels, in which Belousov-Zhabotinsky (BZ) reactions take place under the influence of irradiated light. BZ gels undergo a net displacement that is opposite to the propagation oftraveling waves, since these waves “push” the solvent away from the wave source. Amongregions of different oscillatory frequencies, the highest frequency determines the ultimatedirection of motion of the wave. So, we further studied changes in the frequency of theoscillating reaction upon irradiation of light with different intensities. It is found that thefrequency of the reaction first increases (photoinduction), before it decreases monotonouslyand finally becomes arrested (photoinhibition). Related photosensitive results are reproducedby a two-variable photosensitive Oregonator model. These photosensitive characteristics areused to design the experiment, in which differential irradiation of distinct segments of a BZgel is used to induce spontaneous motion either towards (phototropism) or away from(photophobism) brighter regions. These controlled behaviors are explained on the basis of theintensity-dependent frequency of the reaction, and related changes in the net displacement ofthe gel body (movement towards regions of higher frequency). The experiments andsimulations demonstrate that photosensitive gels can be experimentally controlled bymanipulating these two photoeffects. This approach may be helpful in designing intelligentsoft robots capable of executing bionic functions.
引文
[1] Sagués, F.; Epstein, I. R. Nonlinear chemical dynamics[J]. Dalton transactions,2003,1201-1217.
[2] Chattaraj, P. K. Nonlinear Chemical Dynamics[J].1990,172-182.
[3] Epstein, I. R.; Showalter, K. Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos[J].The Journal of Physical Chemistry,1996,100,13132-13147.
[4] Yoshikawa, K.; Matsubara, Y. Spontaneous oscillation of pH and electrical potential in an oil-watersystem[J]. Journal of the American Chemical Society,1983,105,5967-5969.
[5] Burger, M.; Koros, E. Conditions for the onset of chemical oscillation[J]. The Journal of PhysicalChemistry,1980,84,496-500.
[6] Nitzan, A. Oscillations, multiple steady states, and instabilities in illuminated systems[J]. The Journalof Chemical Physics,1973,59,241.
[7] Thomas, R., On the Relation Between the Logical Structure of Systems and Their Ability to GenerateMultiple Steady States or Sustained Oscillations. In Numerical Methods in the Study of CriticalPhenomena, Dora, J.; Demongeot, J.; Lacolle, B., Eds. Springer Berlin Heidelberg:1981; Vol.9, pp180-193.
[8] Roux, J. C. Experimental studies of bifurcations leading to chaos in the Belousof-Zhabotinskyreaction[J]. Physica D: Nonlinear Phenomena,1983,7,57-68.
[9] Field, R. J.; Gy rgyi, L., Chaos in chemistry and biochemistry[M]. World Scientific,1993.
[10] Petrov, V.; Gaspar, V.; Masere, J.; Showalter, K. Controlling chaos in the Belousov—Zhabotinskyreaction[J]. Nature,1993,361,240-243.
[11] Vastano, J. A.; Pearson, J. E.; Horsthemke, W.; Swinney, H. L. Chemical pattern formation withequal diffusion coefficients[J]. Physics Letters A,1987,124,320-324.
[12] Di Natale, C.; Davide, F. A. M.; D'Amico, A.; Sberveglieri, G.; Nelli, P.; Faglia, G.; Perego, C.Complex chemical pattern recognition with sensor array: the discrimination of vintage years ofwine[J]. Sensors and Actuators B: Chemical,1995,25,801-804.
[13] Lengyel, I.; Epstein, I. R. A chemical approach to designing Turing patterns in reaction-diffusionsystems[J]. Proceedings of the National Academy of Sciences,1992,89,3977-3979.
[14] Castets, V.; Dulos, E.; Boissonade, J.; De Kepper, P. Experimental evidence of a sustained standingTuring-type nonequilibrium chemical pattern[J]. Physical Review Letters,1990,64,2953-2956.
[15] Belousov, B. P. A periodic reaction and its mechanism[J]. Compilation of Abstracts on RadiationMedicine,1959,147,1.
[16] Pomeau, Y.; Roux, J. C.; Rossi, A.; Bachelart, S.; Vidal, C. Intermittent behaviour in theBelousov-Zhabotinsky reaction[J]. Journal de Physique Lettres,1981,42,271-273.
[17] Guderian, A.; Dechert, G.; Zeyer, K. P.; Schneider, F. W. Stochastic Resonance in Chemistry.1. TheBelousov Zhabotinsky Reaction[J]. The Journal of Physical Chemistry,1996,100,4437-4441.
[18] Field, R. J.; Burger, M., Oscillations and traveling waves in chemical systems[M]. Wiley New Yorketc.,1985.
[19] Field, R. J. Limit cycle oscillations in the reversible Oregonator[J]. The Journal of Chemical Physics,1975,63,2289.
[20] Noyes, R. M. Chemical oscillations and instabilities.39. A generalized mechanism forbromate-driven oscillators controlled by bromide[J]. Journal of the American Chemical Society,1980,102,4644-4649.
[21] Belmonte, A. L.; Ouyang, Q.; Flesselles, J.-M. Experimental Survey of Spiral Dynamics in theBelousov-Zhabotinsky Reaction[J]. Journal de Physique II,1997,7,1425-1468.
[22] Pagola, A.; Vidal, C. Wave profile and speed near the core of a target pattern in theBelousov-Zhabotinsky reaction[J]. The Journal of Physical Chemistry,1987,91,501-503.
[23] Vanag, V. K.; Epstein, I. R. Inwardly rotating spiral waves in a reaction-diffusion system[J]. Science,2001,294,835-7.
[24] Yang, L.; Dolnik, M.; Zhabotinsky, A. M.; Epstein, I. R. Pattern formation arising from interactionsbetween Turing and wave instabilities[J]. The Journal of Chemical Physics,2002,117,7259.
[25] Cox, M. P.; Ertl, G.; Imbihl, R. Spatial Self-Organization of Surface Structure during an OscillatingCatalytic Reaction[J]. Physical Review Letters,1985,54,1725-1728.
[26] Rotermund, H. H.; Engel, W.; Kordesch, M.; Ertl, G. Imaging of spatio-temporal pattern evolutionduring carbon monoxide oxidation on platinum[J]. Nature,1990,343,355-357.
[27] Noszticzius, Z.; Wittmann, M.; Stirling, P. Bifurcation from excitability to limit cycle oscillations atthe end of the induction period in the classical Belousov–Zhabotinsky reaction[J]. The Journal ofChemical Physics,1987,86,1922.
[28] Kadar, S.; Wang, J.; Showalter, K. Noise-supported travelling waves in sub-excitable media[J].Nature,1998,391,770-772.
[29] Osada, Y.; Okuzaki, H.; Hori, H. A polymer gel with electrically driven motility[J]. Nature,1992,355,242-244.
[30] Teuscher, C.; Adamatzky, A., Proceedings of the2005Workshop on Unconventional Computing:From Cellular Automata to Wetware[M]. Luniver Press,2005.
[31] Agladze, K.; Aliev, R. R.; Yamaguchi, T.; Yoshikawa, K. Chemical Diode[J]. The Journal ofPhysical Chemistry,1996,100,13895-13897.
[32] Hodgkin, A. L.; Huxley, A. F. A quantitative description of membrane current and its application toconduction and excitation in nerve[J]. The Journal of physiology,1952,117,500.
[33] Davidenko, J. M.; Pertsov, A. V.; Salomonsz, R.; Baxter, W.; Jalife, J. Stationary and drifting spiralwaves of excitation in isolated cardiac muscle[J]. Nature,1992,355,349-51.
[34] Imbihl, R.; Ertl, G. Oscillatory Kinetics in Heterogeneous Catalysis[J]. Chemical Reviews,1995,95,697-733.
[35] Belousov, B., Sb. Ref. Radiat. Med[M]. Medgiz,1958.
[36] Wang, J.; Zhao, J.; Chen, Y.; Gao, Q.; Wang, Y. Coexistence of two bifurcation regimes in a closedferroin-catalyzed Belousov-Zhabotinsky reaction[J]. The journal of physical chemistry. A,2005,109,1374-1381.
[37] Borckmans, P.; De Kepper, P.; Khokhlov, A. R., Chemomechanical instabilities in responsivematerials[M]. Springer,2009.
[38] Epstein, I. R.; Pojman, J. A.; Nicolis, G. An introduction to nonlinear chemical dynamics:oscillations, waves, patterns, and chaos[J]. Physics Today,1999,52,68.
[39] Desai, R. C.; Kapral, R., Dynamics of Self-organized and Self-assembled Structures[M]. CambridgeUniversity Press,2009.
[40] Sekiguchi, T.; Mori, Y.; Hanazaki, I. Photo-response of the (Ru(bpy)3)2+/BrO3-/H+System in aContinuous-Flow Stirred Tank Reactor[J]. Chemistry Letters,1993,1309-1312.
[41] Amemiya, T.; Yamamoto, T.; Ohmori, T.; Yamaguchi, T. Experimental and Model Studies ofOscillations, Photoinduced Transitions, and Steady States in the Ru(bpy)2+3-CatalyzedBelousov Zhabotinsky Reaction under Different Solute Compositions[J]. J. Phys. Chem. A,2002,106,612-620.
[42] Jinguji, M.; Ishihara, M.; Nakazawa, T. Primary process of illumination effect on thetris(bipyridine)ruthenium(2+)-catalyzed Belousov-Zhabotinskii reaction[J]. The Journal of PhysicalChemistry,1992,96,4279-4281.
[43] Showalter, K.; Noyes, R. M.; Bar‐Eli, K. A modified Oregonator model exhibiting complicatedlimit cycle behavior in a flow system[J]. The Journal of Chemical Physics,1978,69,2514.
[44] Jung, P.; H nggi, P. Amplification of small signals via stochastic resonance[J]. Physical Review A,1991,44,8032-8042.
[45] Guderian, A.; Münster, A. F.; Jinguji, M.; Kraus, M.; Schneider, F. W. Resonant chaos control bylight in a chemiluminescent reaction[J]. Chemical Physics Letters,1999,312,440-446.
[46] Kuhnert, L.; Krug, H. J. Kinetics of chemical waves in the acidic bromate-malonicacid-tris(bipyridine)ruthenium(2+) system in comparison with the ferroin system[J]. The Journal ofPhysical Chemistry,1987,91,730-733.
[47] Reddy, M. K. R.; Nagy-Ungvarai, Z.; Mueller, S. C. Effect of Visible Light on Wave Propagation inthe Ruthenium-Catalyzed Belousov-Zhabotinsky Reaction[J]. The Journal of Physical Chemistry,1994,98,12255-12259.
[48] Steinbock, O.; Müller, S. C. Chemical spiral rotation is controlled by light-induced artificial cores[J].Physica A: Statistical Mechanics and its Applications,1992,188,61-67.
[49] Steinbock, O.; Zykov, V. S.; Müller, S. C. Wave propagation in an excitable medium along a line ofa velocity jump[J]. Physical Review E,1993,48,3295-3298.
[50] Petrov, V.; Ouyang, Q.; Swinney, H. L. Resonant pattern formation in achemical system[J]. Nature,1997,388,655-657.
[51] Amemiya, T.; Kádár, S.; Kettunen, P.; Showalter, K. Spiral Wave Formation in Three-DimensionalExcitable Media[J]. Physical Review Letters,1996,77,3244-3247.
[52] Amemiya, T.; Kettunen, P.; Kadar, S.; Yamaguchi, T.; Showalter, K. Formation and evolution ofscroll waves in photosensitive excitable media[J]. Chaos,1998,8,872-878.
[53] Grill, S.; Zykov, V. S.; Müller, S. C. Feedback-Controlled Dynamics of Meandering Spiral Waves[J].Physical Review Letters,1995,75,3368-3371.
[54] Yoshida, R.; Takahashi, T.; Yamaguchi, T.; Ichijo, H. Self-Oscillating Gel[J]. Journal of theAmerican Chemical Society,1996,118,5134-5135.
[55] Maeda, S.; Hara, Y.; Yoshida, R.; Hashimoto, S. Peristaltic Motion of Polymer Gels[J]. AngewandteChemie,2008,120,6792-6795.
[56] Huang, K. T.; Gorska, K.; Alvarez, S.; Barluenga, S.; Winssinger, N. Combinatorial self-assembly ofglycan fragments into microarrays[J]. Chembiochem: a European journal of chemical biology,2011,12,56-60.
[57] Kuhnert, L. A new optical photochemical memory device in a light-sensitive chemical activemedium[J]. Nature,1986,319,393-394.
[58] Kuhnert, L.; Agladze, K. I.; Krinsky, V. I. Image processing using light-sensitive chemical waves[J].Nature,1989,337,244-247.
[59] Steinbock, O.; Zykov, V.; Müller, S. C. Control of spiral-wave dynamics in active media by periodicmodulationof excitability[J]. Nature,1993,366,322-324.
[60] Gray, P.; Scott, S. K., Chemical oscillations and instabilities: non-linear chemical kinetics[M].Clarendon Press. Oxford University Press,1990.
[61] Zhabotinsky, A. Periodic processes of malonic acid oxidation in a liquid phase[J]. Biofizika,1964,9,11.
[62] Demas, J. N.; Diemente, D.; Harris, E. W. Oxygen quenching of charge-transfer excited states ofruthenium(II) complexes. Evidence for singlet oxygen production[J]. Journal of the AmericanChemical Society,1973,95,6864-6865.
[63] Bolletta, F.; Balzani, V. Oscillating chemiluminescence from the reduction of bromate by malonicacid catalyzed by tris(2,2'-bipyridine)ruthenium(II)[J]. Journal of the American Chemical Society,1982,104,4250-4251.
[64] Zeyer, K. P.; Schneider, F. W. Periodicity and Chaos in Chemiluminescence: TheRuthenium-Catalyzed Belousov Zhabotinsky Reaction[J]. J. Phys. Chem. A,1998,102,9702-9709.
[65] Gáspár, V.; Bazsa, G.; Beck, M. The influence of visible light on the Belousov–Zhabotinskiioscillating reactions applying different catalysts[J]. Z. Phys. Chem.(Leipzig),1983,264,43-48.
[66] Delgado, J.; Zhang, Y.; Xu, B.; Epstein, I. R. Terpyridine-and bipyridine-based rutheniumcomplexes as catalysts for the Belousov-Zhabotinsky reaction[J]. The journal of physical chemistry.A,2011,115,2208-15.
[67] Kaminaga, A.; Hanazaki, I. Transient Photoresponse of the Tris(2,2‘-bipyridine)ruthenium(II)-Catalyzed Minimal Bromate Oscillator[J]. J. Phys. Chem. A,1998,102,3307-3314.
[68] Kaminaga, A.; Mori, Y.; Hanazaki, I. Photo-induced excitability in the tris-(bipyridyl)Ru(II)-catalyzed Belousov-Zhabotinsky reaction[J]. Chemical Physics Letters,1997,279,339-343.
[69] Kaminaga, A.; Hanazaki, I. Photo-induced excitability in the tris-(bipyridyl) ruthenium(II)-catalyzedminimal bromate oscillator[J]. Chemical Physics Letters,1997,278,16-20.
[70] Agladze, K.; Obata, S.; Yoshikawa, K. Phase-shift as a basis of image processing in oscillatingchemical medium[J]. Physica D: Nonlinear Phenomena,1995,84,238-245.
[71] Matsumura-Inoue, T.; Nakamura, T.; Mori, Y.; Hanazaki, I. Effect of Pulsed Illumination on theBelousov-Zhabotinsky Reaction Catalyzed with Tris (bipyridine) Ruthenium (II) in ContinuousStirred Tank Reactor[J]. Chemistry Letters,1999,1237-1238.
[72] Huh, D. S.; Choe, Y. M.; Park, D. Y.; Park, S. H.; Zhao, Y. S.; Kim, Y. J.; Yamaguchi, T. Controllingthe Ru-catalyzed Belousov–Zhabotinsky reaction by addition of hydroquinone[J]. Chemical PhysicsLetters,2006,417,555-560.
[73] Delgado, J.; Li, N.; Leda, M.; González-Ochoa, H. O.; Fraden, S.; Epstein, I. R. Coupled oscillationsin a1D emulsion of Belousov–Zhabotinsky droplets[J]. Soft Matter,2011,7,3155.
[74] Vanag, V. K.; Epstein, I. R. Localized patterns in reaction-diffusion systems[J]. Chaos,2007,17,037110.
[75] Nanjundiah, V. Cyclic AMP oscillations in Dictyostelium discoideum: models and observations[J].Biophysical Chemistry,1998,72,1-8.
[76] Bugrim, A. E.; Zhabotinsky, A. M.; Epstein, I. R. Calcium waves in a model with a random spatiallydiscrete distribution of Ca2+release sites[J]. Biophysical Journal,1997,73,2897-2906.
[77] Krug, H. J.; Pohlmann, L.; Kuhnert, L. Analysis of the modified complete Oregonator accountingfor oxygen sensitivity and photosensitivity of Belousov-Zhabotinskii systems[J]. The Journal ofPhysical Chemistry,1990,94,4862-4866.
[78] Nakata, S.; Matsushita, M.; Sato, T.; Suematsu, N. J.; Kitahata, H.; Amemiya, T.; Mori, Y.Photoexcited chemical wave in the ruthenium-catalyzed Belousov-Zhabotinsky reaction[J]. Thejournal of physical chemistry. A,2011,115,7406-12.
[79] Steele, A. J.; Tinsley, M.; Showalter, K. Collective behavior of stabilized reaction-diffusion waves[J].Chaos,2008,18,026108.
[80] Kitahata, H.; Fujio, K.; Gorecki, J.; Nakata, S.; Igarashi, Y.; Gorecka, A.; Yoshikawa, K. Oscillationin Penetration Distance in a Train of Chemical Pulses Propagating in an Optically ConstrainedNarrowing Channel[J]. J. Phys. Chem. A,2009,113,10405-10409.
[81] Kosek, J.; Sevcikova, H.; Marek, M. Splitting of Excitable Pulse Waves[J]. The Journal of PhysicalChemistry,1995,99,6889-6896.
[82] Ram Reddy, M. K.; Dahlem, M.; Zykov, V. S.; Müller, S. C. The effect of an illumination jump onwave propagation in the Ru-catalyzed Belousov-Zhabotinsky reaction[J]. Chemical Physics Letters,1995,236,111-116.
[83] Nakata, S.; Matsushita, M.; Sato, T.; Suematsu, N. J.; Kitahata, H.; Amemiya, T.; Mori, Y.Photoexcited Chemical Wave in the Ruthenium-Catalyzed Belousov–Zhabotinsky Reaction[J]. J.Phys. Chem. A,2011,115,7406-7412.
[84] Kitahata, H.; Yoshikawa, K. Spatio-temporal pattern formation with oscillatory chemical reactionand continuous photon flux on a micrometre scale[J]. Journal of Physics: Condensed Matter,2005,17, S4239-S4248.
[85] Winfree, A. T. Spiral Waves of Chemical Activity[J]. Science,1972,175,634-636.
[86] Bub, G.; Shrier, A.; Glass, L. Spiral Wave Generation in Heterogeneous Excitable Media[J].Physical Review Letters,2002,88,058101.
[87] Petrov, V.; Ouyang, Q.; Li, G.; Swinney, H. L. Light-Induced Frequency Shift in Chemical Spirals[J].The Journal of Physical Chemistry,1996,100,18992-18996.
[88] Aliev, R. R.; Amemiya, T.; Yamaguchi, T. Bifurcation of vortices in the light-sensitive oscillatoryBelousov-Zhabotinsky medium[J]. Chemical Physics Letters,1996,257,552-556.
[89] Braune, M.; Engel, H. Compound rotation of spiral waves in active media with periodicallymodulated excitability[J]. Chemical Physics Letters,1993,211,534-540.
[90] Braune, M.; Engel, H. Compound rotation of spiral waves in a light-sensitive Belousov–Zhabotinsky medium[J]. Chemical Physics Letters,1993,204,257-264.
[91] Braune, M.; Schrader, A.; Engel, H. Entrainment and resonance of spiral waves in active media withperiodically modulated excitability[J]. Chemical Physics Letters,1994,222,358-362.
[92] Brandtst dter, H.; Braune, M.; Schebesch, I.; Engel, H. Experimental study of the dynamics of spiralpairs in light-sensitive Belousov–Zhabotinskii media using an open-gel reactor[J]. Chemical PhysicsLetters,2000,323,145-154.
[93] Agladze, K.; Voignier, V.; Hamm, E.; Plaza, F.; Krinsky, V. Fast Selective Elimination of SpiralWaves[J]. The Journal of Physical Chemistry,1996,100,18764-18769.
[94] Martinez, K.; Lin, A. L.; Kharrazian, R.; Sailer, X.; Swinney, H. L. Resonance in periodicallyinhibited reaction–diffusion systems[J]. Physica D: Nonlinear Phenomena,2002,168-169,1-9.
[95] Markus, M.; Nagy-Ungvarai, Z.; Hess, B. Phototaxis of spiral waves[J]. Science,1992,257,225-7.
[96] Cassidy, I.; Müller, S. C. Desensitization effects in the ruthenium-catalyzed Belousov-Zhabotinskyreaction[J]. Physical Review E,2006,74,026206.
[97] Nakata, S.; Kirisaka, J.; Arima, Y.; Ishii, T. Self-motion of a camphanic acid disk on water withdifferent types of surfactants[J]. The journal of physical chemistry. B,2006,110,21131-4.
[98] Matsushita, M.; Nakata, S.; Kitahata, H. Characteristic features in the collision of chemical wavesdepending on the aspect ratio of a rectangular field[J]. The journal of physical chemistry. A,2007,111,5833-8.
[99] Tanaka, M.; Nagahara, H.; Kitahata, H.; Krinsky, V.; Agladze, K.; Yoshikawa, K. Survival versuscollapse: Abrupt drop of excitability kills the traveling pulse, while gradual change results inadaptation[J]. Physical Review E,2007,76,016205.
[100] Marts, B.; Simpson, D. J. W.; Hagberg, A.; Lin, A. L. Period doubling in a periodically forcedBelousov-Zhabotinsky reaction[J]. Physical Review E,2007,76,026213.
[101] Lin, A. L.; Bertram, M.; Martinez, K.; Swinney, H. L.; Ardelea, A.; Carey, G. F. Resonant phasepatterns in a reaction-diffusion system[J]. Physical review letters,2000,84,4240-4243.
[102] Lin, A. L.; Hagberg, A.; Ardelea, A.; Bertram, M.; Swinney, H. L.; Meron, E. Four-phase patternsin forced oscillatory systems[J]. Physical Review E,2000,62,3790-3798.
[103] Marts, B.; Martinez, K.; Lin, A. L. Front dynamics in an oscillatory bistable Belousov-Zhabotinskychemical reaction[J]. Physical Review E,2004,70,056223.
[104] Nakata, S.; Kashima, K.; Kitahata, H.; Mori, Y. Phase wave between two oscillators in thephotosensitive Belousov-Zhabotinsky reaction depending on the difference in the illuminationtime[J]. The journal of physical chemistry. A,2010,114,9124-9.
[105] Samoilov, M.; Arkin, A.; Ross, J. Signal Processing by Simple Chemical Systems[J]. J. Phys.Chem. A,2002,106,10205-10221.
[106] Ichino, T.; Fujio, K.; Matsushita, M.; Nakata, S. Wave propagation in the photosensitiveBelousov-Zhabotinsky reaction across an asymmetric gap[J]. The journal of physical chemistry. A,2009,113,2304-8.
[107] Nakata, S.; Morishima, S.; Ichino, T.; Kitahata, H. Coexistence of wave propagation and oscillationin the photosensitive Belousov-Zhabotinsky reaction on a circular route[J]. The journal of physicalchemistry. A,2006,110,13475-8.
[108] Sendi a-Nadal, I.; Gómez-Gesteira, M.; Pérez-Mu uzuri, V.; Pérez-Villar, V.; Armero, J.;Ramírez-Piscina, L.; Casademunt, J.; Sagués, F.; Sancho, J. M. Wave competition in excitablemodulated media[J]. Physical Review E,1997,56,6298-6301.
[109] Jinguji, M.; Ishihara, M.; Nakazawa, T.; Nagashima, H. Formation and propagation of rectangularchemical waves in the Belousov-Zhabotinskii reaction[J]. Physica D: Nonlinear Phenomena,1995,84,246-252.
[110] Agladze, K.; Tóth, á.; Ichino, T.; Yoshikawa, K. Propagation of Chemical Waves at the Boundaryof Excitable and Inhibitory Fields[J]. J. Phys. Chem. A,2000,104,6677-6680.
[111] Toth, R.; Stone, C.; Adamatzky, A.; de Lacy Costello, B.; Bull, L. Experimental validation ofbinary collisions between wave fragments in the photosensitive Belousov–Zhabotinsky reaction[J].Chaos, Solitons&Fractals,2009,41,1605-1615.
[112] de Lacy Costello, B.; Toth, R.; Stone, C.; Adamatzky, A.; Bull, L. Implementation of glider guns inthe light-sensitive Belousov-Zhabotinsky medium[J]. Physical Review E,2009,79,026114.
[113] Igarashi, Y.; Gorecki, J.; Gorecka, J. N. One dimensional signal diodes constructed with excitablechemical system[J]. Acta Physica Polonica B,2008,39,1187.
[114] Gorecka, J. N.; Gorecki, J.; Igarashi, Y. One dimensional chemical signal diode constructed withtwo nonexcitable barriers[J]. The journal of physical chemistry. A,2007,111,885-9.
[115] Gorecki, J.; Yoshikawa, K.; Igarashi, Y. On Chemical Reactors That Can Count[J]. J. Phys. Chem.A,2003,107,1664-1669.
[116] Kaminaga, A.; Vanag, V. K.; Epstein, I. R. A Reaction–Diffusion Memory Device[J]. AngewandteChemie International Edition,2006,45,3087-3089.
[117] Davidenko, J. M.; Pertsov, A. V.; Salomonsz, R.; Baxter, W.; Jalife, J. Stationary and drifting spiralwaves of excitation in isolated cardiac muscle[J]. Nature,1992,355,349-351.
[118] Gorelova, N. A.; Bure, J. Spiral waves of spreading depression in the isolated chicken retina[J].Journal of Neurobiology,1983,14,353-363.
[119] Mironov, S.; Vinson, M.; Mulvey, S.; Pertsov, A. Destabilization of Three-Dimensional RotatingChemical Waves in an Inhomogeneous BZ Reaction[J]. The Journal of Physical Chemistry,1996,100,1975-1983.
[120] Field, R. J.; Koros, E.; Noyes, R. M. Oscillations in chemical systems. II. Thorough analysis oftemporal oscillation in the bromate-cerium-malonic acid system[J]. Journal of the AmericanChemical Society,1972,94,8649-8664.
[121] Toth, R.; Taylor, A. F. The tris(2,2′-bipyridyl)ruthenium-catalysed Belousov–Zhabotinskyreaction[J]. Progress in Reaction Kinetics and Mechanism,2006,31,59-115.
[122] Reddy, M. K. R.; Szlavik, Z.; Nagy-Ungvarai, Z.; Muller, S. C. Influence of Light on the InorganicPart of the Ruthenium-Catalyzed Belousov-Zhabotinsky Reaction[J]. The Journal of PhysicalChemistry,1995,99,15081-15085.
[123] Hanazaki, I. Cross section of light-induced inhibition and induction of chemical oscillations[J]. TheJournal of Physical Chemistry,1992,96,5652-5657.
[124] Srivastava, P. K.; Mori, Y.; Hanazaki, I. Photo-inhibition of chemical oscillation in theRu(bpy)2+3-catalyzed Belousov—Zhabotinskii reaction[J]. Chemical Physics Letters,1992,190,279-284.
[125] Zhabotinsky, A. M.; Zaikin, A. N. Autowave processes in a distributed chemical system[J]. Journalof Theoretical Biology,1973,40,45-61.
[126] Yamaguchi, T.; Shimamoto, Y.; Amemiya, T.; Yoshimoto, M.; Ohmori, T.; Nakaiwa, M.; Akiya, T.;Sato, M.; Matsumura-Inoue, T. Bromomalonic acid as a source of photochemically produced Brion in the Ru(bpy)32+-catalyzed Belousov-Zhabotinsky reaction[J]. Chemical Physics Letters,1996,259,219-224.
[127] Kádár, S.; Amemiya, T.; Showalter, K. Reaction Mechanism for Light Sensitivity of theRu(bpy)32+-Catalyzed Belousov Zhabotinsky Reaction[J]. J. Phys. Chem. A,1997,101,8200-8206.
[128] Vanag, V. K.; Zhabotinsky, A. M.; Epstein, I. R. Pattern Formation in the Belousov ZhabotinskyReaction with Photochemical Global Feedback[J]. J. Phys. Chem. A,2000,104,11566-11577.
[129] Treindl, L.; Knudsen, D.; Nakamura, T.; Matsumura-Inoue, T.; J rgensen, K. B.; Ruoff, P. TheLight-Perturbed Ru-Catalyzed Belousov Zhabotinsky Reaction: Evidence for PhotochemicallyProduced Bromous Acid and Bromide Ions by Phase Response Analysis[J]. J. Phys. Chem. A,2000,104,10783-10788.
[130] Hanazaki, I.; Kaminaga, A.; Mori, Y.; Rabai, G. Response of some chemical oscillators to thepulsed light perturbation[J]. ACH, models in chemistry,1998,135,257-268.
[131] Field, R. J. Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemicalreaction[J]. The Journal of Chemical Physics,1974,60,1877.
[132] Bao, W.; Li, Z.; Zhou, L.-Q.; Gao, Z. Robust entrainment phenomena of oscillations by delay timein the photosensitive Oregonator model[J]. Physical Review E,2009,79,016214.
[133] Kheowan, O.-U.; Chan, C.-K.; Zykov, V. S.; Rangsiman, O.; Müller, S. C. Spiral wave dynamicsunder feedback derived from a confined circular domain[J]. Physical Review E,2001,64,035201.
[134] Zhou, L.-Q.; Cassidy, I.; Müller, S. C.; Cheng, X.; Huang, G.; Ouyang, Q. Frequency-LockingPhenomena of Propagating Wave Fronts in Reaction-Diffusion Systems[J]. Physical ReviewLetters,2005,94,128301.
[135] Amemiya, T.; Ohmori, T.; Yamaguchi, T. An Oregonator-Class Model for Photoinduced Behaviorin the Ru(bpy)32+-Catalyzed Belousov Zhabotinsky Reaction[J]. J. Phys. Chem. A,2000,104,336-344.
[136] Amemiya, T.; Ohmori, T.; Nakaiwa, M.; Yamaguchi, T. Two-Parameter Stochastic Resonance in aModel of the Photosensitive Belousov Zhabotinsky Reaction in a Flow System[J]. J. Phys. Chem.A,1998,102,4537-4542.
[137] Rovinskii, A. B.; Zhabotinskii, A. M. Mechanism and mathematical model of the oscillatingbromate-ferroin-bromomalonic acid reaction[J]. The Journal of Physical Chemistry,1984,88,6081-6084.
[138] Zhabotinsky, A. M.; Buchholtz, F.; Kiyatkin, A. B.; Epstein, I. R. Oscillations and waves inmetal-ion-catalyzed bromate oscillating reactions in highly oxidized states[J]. The Journal ofPhysical Chemistry,1993,97,7578-7584.
[139] Tanaka, T. Collapse of Gels and the Critical Endpoint[J]. Physical Review Letters,1978,40,820-823.
[140] Kokufuta, E.; Zhang, Y.-Q.; Tanaka, T. Biochemo-mechanical function of urease-loaded gels[J].Journal of Biomaterials Science, Polymer Edition,1995,6,35-40.
[141] Yoshida, R. Design of Functional Polymer Gels and Their Application to Biomimetic Materials[J].Current Organic Chemistry,2005,9,1617-1641.
[142] Kishi, R.; Ichijo, H.; Hirasa, O. Thermo-responsive devices using poly (vinyl methyl ether)hydrogels[J]. Journal of intelligent material systems and structures,1993,4,533-537.
[143] Okano, T.; Bae, Y. H.; Jacobs, H.; Kim, S. W. Thermally on-off switching polymers for drugpermeation and release[J]. Journal of Controlled Release,1990,11,255-265.
[144] Peppas, N. Hydrogels in pharmaceutical formulations[J]. European Journal of Pharmaceutics andBiopharmaceutics,2000,50,27-46.
[145] Yoshida, R. Gels coupled to oscillatory reactions[J]. Nonlinear Dynamics with Polymers:Fundamentals, Methods and Applications,2011,115-134.
[146] Yoshida, R.; Kokufuta, E.; Yamaguchi, T. Beating polymer gels coupled with a nonlinear chemicalreaction[J]. Chaos,1999,9,260-266.
[147] Crook, C. J.; Smith, A.; Jones, R. A.; Ryan, A. J. Chemically induced oscillations in apH-responsive hydrogel[J]. Physical Chemistry Chemical Physics,2002,4,1367-1369.
[148] Yoshida, R.; Ichijo, H.; Hakuta, T.; Yamaguchi, T. Self-oscillating swelling and deswelling ofpolymer gels[J]. Macromolecular Rapid Communications,1995,16,305-310.
[149] Crook, C. J.; Smith, A.; Jones, R. A. L.; Ryan, A. J. Chemically induced oscillations in apH-responsive hydrogel[J]. Physical Chemistry Chemical Physics,2002,4,1367-1369.
[150] Wang, J.; Zhao, J.; Chen, Y.; Gao, Q.; Wang, Y. Coexistence of two bifurcation regimes in a closedferroin-catalyzed Belousov-Zhabotinsky reaction[J]. The journal of physical chemistry. A,2005,109,1374-81.
[151] Zhang, D.; Gyorgyi, L.; Peltier, W. R. Deterministic chaos in the Belousov-Zhabotinsky reaction:Experiments and simulations[J]. Chaos,1993,3,723-745.
[152] Epstein, I. R. Spiral waves in chemistry and biology[J]. Science,1991,252,67.
[153] Váradi, Z.; Beck, M. T. Inhibition of a homogeneous periodic reaction by radical scavengers[J].Journal of the Chemical Society, Chemical Communications,1973,30-31.
[154] Pojman, J. A.; Ilyashenko, V. M.; Khan, A. M. Free-radical frontal polymerization: self-propagatingthermal reaction waves[J]. J. Chem. Soc., Faraday Trans.,1996,92,2825-2837.
[155] Tabata, O.; Hirasawa, H.; Aoki, S.; Yoshida, R.; Kokufuta, E. Ciliary motion actuator usingself-oscillating gel[J]. Sensors and Actuators A: Physical,2002,95,234-238.
[156] Murase, Y.; Maeda, S.; Hashimoto, S.; Yoshida, R. Design of a mass transport surface utilizingperistaltic motion of a self-oscillating gel[J]. Langmuir: the ACS journal of surfaces and colloids,2009,25,483-9.
[157] Ghosh, P.; Spiro, T. G. Photoelectrochemistry of tris(bipyridyl)ruthenium(II) covalently attached ton-type tin(IV) oxide[J]. Journal of the American Chemical Society,1980,102,5543-5549.
[158] Sakai, T.; Yoshida, R. Self-Oscillating Nanogel Particles[J]. Langmuir: the ACS journal ofsurfaces and colloids,2004,20,1036-1038.
[159] Yoshida, R. Self-Oscillating Gels Driven by the Belousov–Zhabotinsky Reaction as Novel SmartMaterials[J]. Advanced Materials,2010,22,3463-3483.
[160] Tabata, O.; Kojima, H.; Kasatani, T.; Isono, Y.; Yoshida, R. Chemo-mechanical actuator usingself-oscillating gel for artificial cilia[J].2003,12-15.
[161] Murase, Y.; Hidaka, M.; Yoshida, R. Self-driven gel conveyer: Autonomous transportation byperistaltic motion of self-oscillating gel[J]. Sensors and Actuators B: Chemical,2010,149,272-283.
[162] Shinohara, S.-i.; Seki, T.; Sakai, T.; Yoshida, R.; Takeoka, Y. Photoregulated Wormlike Motion of aGel[J]. Angewandte Chemie,2008,120,9179-9183.
[163] Maeda, S.; Hara, Y.; Sakai, T.; Yoshida, R.; Hashimoto, S. Self-Walking Gel[J]. AdvancedMaterials,2007,19,3480-3484.
[164] Zaikin, A. N.; Zhabotinsky, A. M. Concentration Wave Propagation in Two-dimensionalLiquid-phase Self-oscillating System[J]. Nature,1970,225,535-537.
[165] Yoshida, R.; Tanaka, M.; Onodera, S.; Yamaguchi, T.; Kokufuta, E. In-Phase Synchronization ofChemical and Mechanical Oscillations in Self-Oscillating Gels[J]. J. Phys. Chem. A,2000,104,7549-7555.
[166] Tateyama, S.; Shibuta, Y.; Yoshida, R. Direction control of chemical wave propagation inself-oscillating gel array[J]. The journal of physical chemistry. B,2008,112,1777-82.
[167] Yoshida, R.; Sakai, T.; Hara, Y.; Maeda, S.; Hashimoto, S.; Suzuki, D.; Murase, Y. Self-oscillatinggel as novel biomimetic materials[J]. Journal of controlled release: official journal of theControlled Release Society,2009,140,186-93.
[168] Sakai, T.; Takeoka, Y.; Seki, T.; Yoshida, R. Organized monolayer of thermosensitive microgelbeads prepared by double-template polymerization[J]. Langmuir: the ACS journal of surfaces andcolloids,2007,23,8651-4.
[169] Yoshida, R.; Sakai, T.; Tambata, O.; Yamaguchi, T. Design of novel biomimetic polymer gels withself-oscillating function[J]. Science and Technology of Advanced Materials,2002,3,95-102.
[170] Ito, Y.; Nogawa, M.; Yoshida, R. Temperature Control of the Belousov Zhabotinsky ReactionUsing a Thermoresponsive Polymer[J]. Langmuir: the ACS journal of surfaces and colloids,2003,19,9577-9579.
[171] Sasaki, S.; Koga, S.; Yoshida, R.; Yamaguchi, T. Mechanical Oscillation Coupled with theBelousov Zhabotinsky Reaction in Gel[J]. Langmuir: the ACS journal of surfaces and colloids,2003,19,5595-5600.
[172] Maeda, S.; Hara, Y.; Yoshida, R.; Hashimoto, S. Control of the Dynamic Motion of a Gel ActuatorDriven by the Belousov-Zhabotinsky Reaction[J]. Macromolecular Rapid Communications,2008,29,401-405.
[173] Yoshida, R.; Omata, K.; Yamaura, K.; Ebata, M.; Tanaka, M.; Takai, M. Maskless microfabricationof thermosensitive gels using a microscope and application to a controlled release microchip[J].Lab on a chip,2006,6,1384-6.
[174] Hara, Y.; Yoshida, R. Self-oscillation of polymer chains induced by the Belousov-Zhabotinskyreaction under acid-free conditions[J]. The journal of physical chemistry. B,2005,109,9451-4.
[175] Yashin, V. V.; Balazs, A. C. Theoretical and computational modeling of self-oscillating polymergels[J]. J Chem Phys,2007,126,124707.
[176] Yashin, V. V.; Balazs, A. C. Modeling Polymer Gels Exhibiting Self-Oscillations Due to theBelousov Zhabotinsky Reaction[J]. Macromolecules,2006,39,2024-2026.
[177] Yashin, V. V.; Kuksenok, O.; Balazs, A. C. Modeling autonomously oscillating chemo-responsivegels[J]. Progress in Polymer Science,2010,35,155-173.
[178] Yashin, V. V.; Balazs, A. C. Pattern formation and shape changes in self-oscillating polymer gels[J].Science,2006,314,798-801.
[179] Yashin, V. V.; Balazs, A. C. Chemomechanical synchronization in heterogeneous self-oscillatinggels[J]. Physical Review E,2008,77,046210.
[180] Kuksenok, O.; Yashin, V. V.; Balazs, A. C. Three-dimensional model for chemoresponsive polymergels undergoing the Belousov-Zhabotinsky reaction[J]. Physical Review E,2008,78,041406.
[181] Yashin, V. V.; Van Vliet, K. J.; Balazs, A. C. Controlling chemical oscillations in heterogeneousBelousov-Zhabotinsky gels via mechanical strain[J]. Physical Review E,2009,79,046214.
[182] Kuksenok, O.; Yashin, V. V.; Balazs, A. C. Mechanically induced chemical oscillations and motionin responsive gels[J]. Soft Matter,2007,3,1138.
[183] Kuksenok, O.; Yashin, V. V.; Balazs, A. C. Global signaling of localized impact inchemo-responsive gels[J]. Soft Matter,2009,5,1835.
[184] Dayal, P.; Kuksenok, O.; Balazs, A. C. Designing autonomously motile gels that follow complexpaths[J]. Soft Matter,2010,6,768.
[185] Dayal, P.; Kuksenok, O.; Balazs, A. C. Using light to guide the self-sustained motion of activegels[J]. Langmuir: the ACS journal of surfaces and colloids,2009,25,4298-301.
[186] Chen, I. C.; Kuksenok, O.; Yashin, V. V.; Moslin, R. M.; Balazs, A. C.; Van Vliet, K. J. Shape-andsize-dependent patterns in self-oscillating polymer gels[J]. Soft Matter,2011,7,3141.
[187] Nettesheim, S.; von Oertzen, A.; Rotermund, H. H.; Ertl, G. Reaction diffusion patterns in thecatalytic CO-oxidation on Pt(110): Front propagation and spiral waves[J]. The Journal of ChemicalPhysics,1993,98,9977.
[188] Keener, J. P.; Tyson, J. J. Spiral waves in the Belousov-Zhabotinskii reaction[J]. Physica D:Nonlinear Phenomena,1986,21,307-324.
[189] Horvath, J.; Szalai, I.; De Kepper, P. An experimental design method leading to chemical Turingpatterns[J]. Science,2009,324,772-5.
[190] Bursac, N.; Aguel, F.; Tung, L. Multiarm spirals in a two-dimensional cardiac substrate[J].Proceedings of the National Academy of Sciences of the United States of America,2004,101,15530-4.
[191] Vanag, V.; Epstein, I. Pattern Formation in a Tunable Medium: The Belousov-ZhabotinskyReaction in an Aerosol OT Microemulsion[J]. Physical Review Letters,2001,87.
[192] Vanag, V. K.; Epstein, I. R. Packet Waves in a Reaction-Diffusion System[J]. Physical ReviewLetters,2002,88,088303.
[193] Vanag, V. K.; Yang, L.; Dolnik, M.; Zhabotinsky, A. M.; Epstein, I. R. Oscillatory cluster patternsin a homogeneous chemical system with global feedback[J]. Nature,2000,406,389-391.
[194] Capadona, J. R.; Shanmuganathan, K.; Tyler, D. J.; Rowan, S. J.; Weder, C. Stimuli-responsivepolymer nanocomposites inspired by the sea cucumber dermis[J]. Science,2008,319,1370-4.
[195] Beebe, D. J.; Moore, J. S.; Bauer, J. M.; Yu, Q.; Liu, R. H.; Devadoss, C.; Jo, B.-H. Functionalhydrogel structures for autonomous flow control inside microfluidic channels[J]. Nature,2000,404,588-590.
[196] Ichino, T.; Asahi, T.; Kitahata, H.; Magome, N.; Agladze, K.; Yoshikawa, K. MicrofreightDelivered by Chemical Waves[J]. Journal of Physical Chemistry C,2008,112,3032-3035.
[197] Fu, A. K.; Hung, K. W.; Fu, W. Y.; Shen, C.; Chen, Y.; Xia, J.; Lai, K. O.; Ip, N. Y. APC(Cdh1)mediates EphA4-dependent downregulation of AMPA receptors in homeostatic plasticity[J].Nature neuroscience,2011,14,181-9.
[198] Shi, L.; Butt, B.; Ip, F. C.; Dai, Y.; Jiang, L.; Yung, W. H.; Greenberg, M. E.; Fu, A. K.; Ip, N. Y.Ephexin1is required for structural maturation and neurotransmission at the neuromuscularjunction[J]. Neuron,2010,65,204-16.
[199] Croker, J. L.; Witte, W. T.; Auge, R. M. Stomatal sensitivity of six temperate, deciduous treespecies to non-hydraulic root-to-shoot signalling of partial soil drying[J]. Journal of ExperimentalBotany,1998,49,761-774.
[200] Jackson, M. B.; Armstrong, W. Formation of Aerenchyma and the Processes of Plant Ventilation inRelation to Soil Flooding and Submergence[J]. Plant Biology,1999,1,274-287.
[201] Winfree, A. T. The prehistory of the Belousov-Zhabotinsky oscillator[J]. Journal of ChemicalEducation,1984,61,661.
[202] Tóth, á.; Horváth, D.; Yoshikawa, K. Unidirectional wave propagation in one spatial dimension[J].Chemical Physics Letters,2001,345,471-474.
[203] Toth, A.; Gaspar, V.; Showalter, K. Signal transmission in chemical systems: propagation ofchemical waves through capillary tubes[J]. The Journal of Physical Chemistry,1994,98,522-531.
[204] Kitahata, H.; Aihara, R.; Mori, Y.; Yoshikawa, K. Slowing and Stopping of Chemical Waves in aNarrowing Canal[J]. The Journal of Physical Chemistry B,2004,108,18956-18959.
[205] Panfilov, A.; Hogeweg, P. Spiral breakup in a modified FitzHugh-Nagumo model[J]. PhysicsLetters A,1993,176,295-299.
[206] Hastings, S. P. Single and Multiple Pulse Waves for the FitzHugh–Nagumo[J]. SIAM Journal onApplied Mathematics,1982,42,247-260.
[207] Gy rgyi, L.; Field, R. J. A three-variable model of deterministic chaos in theBelousov–Zhabotinsky reaction[J]. Nature,1992,355,808-810.
[208] Ruoff, P. Antagonistic balance in the oregonator: about the possibility of temperature-compensationin the Belousov-Zhabotinsky reaction[J]. Physica D: Nonlinear Phenomena,1995,84,204-211.
[209] Jahnke, W.; Skaggs, W. E.; Winfree, A. T. Chemical vortex dynamics in the Belousov-Zhabotinskiireaction and in the two-variable oregonator model[J]. The Journal of Physical Chemistry,1989,93,740-749.
[210] Winfree, A. T.; Jahnke, W. Three-dimensional scroll ring dynamics in the Belousov-Zhabotinskiireagent and in the two-variable Oregonator model[J]. The Journal of Physical Chemistry,1989,93,2823-2832.
[211] Seifritz, E.; Esposito, F.; Hennel, F.; Mustovic, H.; Neuhoff, J. G.; Bilecen, D.; Tedeschi, G.;Scheffler, K.; Di Salle, F. Spatiotemporal pattern of neural processing in the human auditorycortex[J]. Science,2002,297,1706-8.
[212] Jirsa, V.; Kelso, J. Spatiotemporal pattern formation in neural systems with heterogeneousconnection topologies[J]. Physical Review E,2000,62,8462-8465.
[213] Okano, T., Biorelated polymers and gels: controlled release and applications in biomedicalengineering[M]. Academic Press,1998.
[214] Yui, N., Supramolecular design for biological applications[M]. CRC Press,2002.
[215] Peppas, N. A.; Hilt, J. Z.; Khademhosseini, A.; Langer, R. Hydrogels in Biology and Medicine:From Molecular Principles to Bionanotechnology[J]. Advanced Materials,2006,18,1345-1360.
[216] Yamaguchi, T.; Kuhnert, L.; Nagy-Ungvarai, Z.; Mueller, S. C.; Hess, B. Gel systems for theBelousov-Zhabotinskii reaction[J]. The Journal of Physical Chemistry,1991,95,5831-5837.
[217] Kaminaga, A.; Rábai, G.; Mori, Y.; Hanazaki, I. Photoresponse of theFerrocyanide Bromate Sulfite Chemical Oscillator under Flow Conditions[J]. The Journal ofPhysical Chemistry,1996,100,9389-9394.
[218] Mori, Y.; Nakamichi, Y.; Sekiguchi, T.; Okazaki, N.; Matsumura, T.; Hanazaki, I. Photo-inductionof chemical oscillation in the Belousov—Zhabotinsky reaction under the flow condition[J].Chemical Physics Letters,1993,211,421-424.
[219] Tyson, J. J.; Fife, P. C. Target patterns in a realistic model of the Belousov–Zhabotinskii reaction[J].The Journal of Chemical Physics,1980,73,2224.
[220] Kettunen, P.; Yamaguchi, T.; Hashimoto, H.; Amemiya, T.; Steinbock, B.; Muller, S. C. Emergentreaction-diffusion phenomena in capillary tubes[J]. Chaos,2006,16,037111.