Some remarks on chaos of a coupled lattice system related with the Belusov–Zhabotinskii reaction

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• 作者：Risong Li ; Yu Zhao ; Ru Jiang ; Hongqing Wang
• 关键词：Coupled map lattice ; Devaney’s chaos ; Topologically mixing ; Topologically exact
• 刊名：Journal of Mathematical Chemistry
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：54
• 期：4
• 页码：849-853
• 全文大小：354 KB
• 参考文献：1.T.Y. Li, J.A. Yorke, Period three implies chaos. Am. Math. Mon. 82(10), 985–992 (1975)CrossRef
  2.L.S. Block, W.A. Coppel, Dynamics in One Dimension, Springer Monographs in Mathematics (Springer, Berlin, 1992)
  3.R.L. Devaney, An Introduction to Chaotics Dynamical Systems (Benjamin/Cummings, Menlo Park, 1986)
  4.J.R. Chazottes, B. FernSndez, in Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems, ed. by J.-R. Chazottes, B. Fernandez. Lecture Notes in Physics, vol. 671 (Springer Berlin Heidelberg, New York, 2005)
  5.J.L.G. Guirao, M. Lampart, Chaos of a coupled lattice system related with Belusov–Zhabotinskii reaction. J. Math. Chem. 48, 159–164 (2010)CrossRef
  6.K. Kaneko, Globally coupled chaos violates law of large numbers. Phys. Rev. Lett. 65, 1391–1394 (1990)CrossRef
  7.R. Li, Y. Zhao, Remark on positive entropy of a coupled lattice system related with Belusov–Zhabotinskii reaction. J. Math. Chem. doi:10.​1007/​s10910-015-0538-y
  8.M. Kohmoto, Y. Oono, Discrete model of chemical turbulence. Phys. Rev. Lett. 55, 2927–2931 (1985)CrossRef
  9.J.L. Hudson, M. Hart, D. Marinko, An experimental study of multiplex peak periodic and nonperiodic oscilations in the Belusov–Zhabotinskii reaction. J. Chem. Phys. 71, 1601–1606 (1979)CrossRef
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• 作者单位：Risong Li (1)
  Yu Zhao (1)
  Ru Jiang (1)
  Hongqing Wang (1)
  
  1. School of Science, Guangdong Ocean University, Zhanjiang, 524025, People’s Republic of China
  
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

Guirao and Lampart (J Math Chem 48:159–164, 2010) presented a lattice dynamical system stated by Kaneko (Phys Rev Lett 65:1391–1394, 1990) which is related to the Belusov–Zhabotinskii reaction. Motivated by Guirao and Lampart (J Math Chem 48:159–164, 2010) and Li and Zhao (J Math Chem. doi:10.​1007/​s10910-015-0538-y), in this paper we study the following more general lattice dynamical systems: $$\begin{aligned} y_{i}^{j+1}=(1-\eta )h_{i}\left( y_{i}^{j}\right) +\frac{1}{2}\eta \left[ h_{i}\left( y_{i-1}^{j}\right) -h_{i}\left( y_{i+1}^{j}\right) \right] , \end{aligned}$$where j is discrete time index, i is lattice side index with system size H, \(\eta \in J=[0, 1]\) is coupling constant and \(h_{i}\) is a continuous selfmap on J for any \(i\in \{1, 2, \ldots , H\}\). In particular, we obtain that the following hold:(1) For zero coupling constant, if \(h_{i}\) is topologically exact for any \(i\in \{1, 2, \ldots , H\}\), then so does the above system.