拉伸式3-D多涡卷混沌系统的设计及其在保密通信中的应用
|
摘要
基于典型的Chua式电路,提出了一种拉伸式多涡卷混沌系统。首先,通过系统的对称性、不变性、耗散性、系统平衡点和稳定性,分析了混沌的分维特性、时域波形、Lyapunov指数谱等基本的混沌动力学特性。其次,利用PSPICE实现了该系统的混沌电路。最后,结合Lyapunov稳定性原理,运用单向耦合法,探究了该混沌系统的同步性问题,并采用该方法有效地实现了特定信号的加密、解密。数值仿真与实验结果保持一致,进一步证实了该方法的可行性。
A kind of tensile-type 3-D multi-scroll chaotic attractor based on Chua's circuit was successfully designed. The chaos generation mechanism was studied by analyzing the symmetry and invariance, the existence of the dissipation, as well as the system equilibrium and stability. Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. At the same time, the chaotic circuit of this system was realized by PSPICE. Finally, based on Lyapunov theorem and unidirectionally coupled method, the synchronization of the chaotic system has also been investigated. With this approach, the novel system can be applied to secure communication, which can achieve the purpose of covering specific signals. The experimental results are in agreement with numerical simulation results, which verifies the availability and feasibility of this method.
A kind of tensile-type 3-D multi-scroll chaotic attractor based on Chua's circuit was successfully designed. The chaos generation mechanism was studied by analyzing the symmetry and invariance, the existence of the dissipation, as well as the system equilibrium and stability. Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. At the same time, the chaotic circuit of this system was realized by PSPICE. Finally, based on Lyapunov theorem and unidirectionally coupled method, the synchronization of the chaotic system has also been investigated. With this approach, the novel system can be applied to secure communication, which can achieve the purpose of covering specific signals. The experimental results are in agreement with numerical simulation results, which verifies the availability and feasibility of this method.
引文
[1]LORENZ E N.Deterministic nonperiodic flow[J].Journal of the Atmospheric Sciences,1963,20(2):130-141.
[2]KOCAREV L,HALLE K S,ECKERT K.Experimental demonstration of secure communications via chaotic synchronization[J].International Journal of Bifurcation and Chaos,1992,2(3):709-713.
[3]LU J H,YU X H,CHEN G R.Chaos synchronization of general complex networks dynamical[J].Physica A,2004,334(1):281-302.
[4]TIMMER J,RUST H,HORBELT W,et al.Parametric,nonparametric and parametric modelling of a chaotic circuit time series[J].Physics Letters A,2000,274(3):123-134.
[5]PECORA L M,CARROLL T L.Synchronization in chaotic systems[J].Phys Rev Lett,1900,64(8):821-824.
[6]王兴元,段朝锋.基于线性状态观测器的混沌同步及其在保密通信中的应用[J].通信学报,2005,26(6):105-111.WANG X Y,DUAN C F.Observer based chaos synchronization and its application to secure communication[J].Journal on Communications,2005,26(6):105-111.
[7]WANG X Y,LI X G.Feedback control of Liu chaotic dynamical system[J].International Journal of Modern Physics B,2010,24(3):397-404.
[8]闵国旗,王丽丹,段书凯.离子迁移忆阻混沌电路及其在语音保密通信中的应用[J].物理学报,2015,64(21):210507.MIN G Q,WANG L D,DUAN S K.The chaotic circuit of ion migration memristor and its application in the voice secure communication[J].Acta Phys Sin,2015,64(21):210507.
[9]王兴元.混沌系统的同步及在保密通信中的应用[M].北京:科学出版社,2012:16-80.WANG X Y.The synchronization of chaotic system and its application in secure communication[M].Beijing:Science Press,2012:16-80.
[10]CHEN G,UETA T.Yet another chaotic attractor[J].International Journal of Bifurcation and Chaos,1999,9(7):1465-1466.
[11]YALCIN M E.Multi-scroll and hyper-cube attractors from a general jerk circuit using Josephson junctions[J].Chaos,Solitons&Fractals,2007,34(5):1659-1666.
[12]LU J,CHEN G.A new chaotic attractor coined[J].International Journal of Bifurcation and Chaos,2002,12(03):659-661.
[13]MATSUMOTO T,CHUA L O,TANAKA S.Simplest chaotic nonautonomous circuit[J].Physical Review A,1984,30(2):1155-1157.
[14]BILOTTA E,PANTANO P,STRANGES F.A gallery of Chua attractors:part I[J].International Journal of Bifurcation and Chaos,2007,17(1):1-60.
[15]SUYKENS J A K,CHUA L O.N-double scroll hyper-cubes in 1-D CNNS[J].International Journal of Bifurcation and Chaos,1997,7(08):1873-1885.
[16]LAMARQUE C H,JANIN O,AWREJCEWICZ J.Chua systems with discontinuities[J].International Journal of Bifurcation and Chaos,1999,9(4):591-616.
[17]MAHLA A I,BADAN PALHARESáG.Chua's circuit with a discontinuous nonlinearity[J].Journal of Circuits,Systems,and Computers,1993,3(1):231-237.
[18]SUYKENS J A K,VANDEWALLE J.Generation of n-double scrolls[J].Circuits and Systems I:Fundamental Theory and Applications,IEEE Transactions on,1993,40(11):861-867.
[19]YIN Y Z.Synchronization of chaos in a modified Chua’s circuit using continuous control[J].International Journal of Bifurcation and Chaos,1996,6(11):2101-2117.
[20]刘明华,禹思敏.多涡卷高阶广义Jerk电路[J].物理学报,2006,55(11):5707-5713.LIU M H,YU S M.Multi-scroll high-order general Jerk circuits[J].Acta Phys Sin,2006,55(11):5707-5713.
[21]李亚,禹思敏,戴青云.一种新的蔡氏电路设计方法与硬件实现[J].物理学报,2006,55(8):3938-3944.LI Y,YU S M,DAI Q Y.A novel approach for Chua’s circuit design and its hardware implementation[J].Acta Phys Sin,2006,55(8):3938-3944.
[22]SAKTHIVEL G,RAJASEKAR S,THAMILMARAN K.Statistical measures and diffusion dynamics in a modified Chua’s circuit equation with multi-scroll attractors[J].International Journal of Bifurcation and Chaos,2012,22(1):1250004.
[23]TANG K S,ZHONG G Q,CHEN G.Generation of n-scroll attractors via sine function[J].IEEE Trans.Circuits Syst-I,2001,48(11):1369-1372.
[24]PENG Z,WANG C,LUO X.A novel multi-directional multi-scroll chaotic system and its CCII+circuit implementation[J].Optik-International Journal for Light and Electron Optics,2014,125(22):6665-6671.
[25]WANG C,LUO X,WAN Z.Generation and circuit implementation of multi-block multi-directional grid multi-scroll chaotic attractors[J].Optic-International Journal for Light and Electron Optics,2014,125(22):6716-6721.
[26]毛学志,徐勇,刘建平.基于反正切的网格混沌吸引子及其保密通信[J].通信学报,2014,35(12):106-115.MAO X Z,XU Y,LIU J P.Grid chaotic attractors based on arc tangent and its secure communication[J].Journal on Communications,2014,35(12):106-115.
[27]于娜,丁群,陈红.异结构系统混沌同步及其在保密通信中的应用[J].通信学报,2007,28(10):73-78.YU N,DING Q,CHEN H.Synchronization of different structure chaotic systems and the application in secure communication[J].Journal on Communication,2007,28(10):73-78.
[28]MA Y,LI Y,JIANG X.Simulation and circuit implementation of12-scroll chaotic system[J].Chaos,Solitons&Fractals,2015,75:127-133.
[29]LI H,WANG L,DUAN S.A memristor-based scroll chaotic system-design,analysis and circuit implementation[J].International Journal of Bifurcation and Chaos,2014,24(07):1450099.
[30]孙克辉.混沌保密通信原理与技术[M].北京:清华大学出版社,2015:58-110.SUN K H.Principle and technology of chaotic secure communication[M].Beijing:Tsinghua University Press,2015:58-110.作者简介:马均澎(1991-),男,山西运城人,西南大学硕士生,主要研究方向为混沌电路设计、非线性系统控制。
[2]KOCAREV L,HALLE K S,ECKERT K.Experimental demonstration of secure communications via chaotic synchronization[J].International Journal of Bifurcation and Chaos,1992,2(3):709-713.
[3]LU J H,YU X H,CHEN G R.Chaos synchronization of general complex networks dynamical[J].Physica A,2004,334(1):281-302.
[4]TIMMER J,RUST H,HORBELT W,et al.Parametric,nonparametric and parametric modelling of a chaotic circuit time series[J].Physics Letters A,2000,274(3):123-134.
[5]PECORA L M,CARROLL T L.Synchronization in chaotic systems[J].Phys Rev Lett,1900,64(8):821-824.
[6]王兴元,段朝锋.基于线性状态观测器的混沌同步及其在保密通信中的应用[J].通信学报,2005,26(6):105-111.WANG X Y,DUAN C F.Observer based chaos synchronization and its application to secure communication[J].Journal on Communications,2005,26(6):105-111.
[7]WANG X Y,LI X G.Feedback control of Liu chaotic dynamical system[J].International Journal of Modern Physics B,2010,24(3):397-404.
[8]闵国旗,王丽丹,段书凯.离子迁移忆阻混沌电路及其在语音保密通信中的应用[J].物理学报,2015,64(21):210507.MIN G Q,WANG L D,DUAN S K.The chaotic circuit of ion migration memristor and its application in the voice secure communication[J].Acta Phys Sin,2015,64(21):210507.
[9]王兴元.混沌系统的同步及在保密通信中的应用[M].北京:科学出版社,2012:16-80.WANG X Y.The synchronization of chaotic system and its application in secure communication[M].Beijing:Science Press,2012:16-80.
[10]CHEN G,UETA T.Yet another chaotic attractor[J].International Journal of Bifurcation and Chaos,1999,9(7):1465-1466.
[11]YALCIN M E.Multi-scroll and hyper-cube attractors from a general jerk circuit using Josephson junctions[J].Chaos,Solitons&Fractals,2007,34(5):1659-1666.
[12]LU J,CHEN G.A new chaotic attractor coined[J].International Journal of Bifurcation and Chaos,2002,12(03):659-661.
[13]MATSUMOTO T,CHUA L O,TANAKA S.Simplest chaotic nonautonomous circuit[J].Physical Review A,1984,30(2):1155-1157.
[14]BILOTTA E,PANTANO P,STRANGES F.A gallery of Chua attractors:part I[J].International Journal of Bifurcation and Chaos,2007,17(1):1-60.
[15]SUYKENS J A K,CHUA L O.N-double scroll hyper-cubes in 1-D CNNS[J].International Journal of Bifurcation and Chaos,1997,7(08):1873-1885.
[16]LAMARQUE C H,JANIN O,AWREJCEWICZ J.Chua systems with discontinuities[J].International Journal of Bifurcation and Chaos,1999,9(4):591-616.
[17]MAHLA A I,BADAN PALHARESáG.Chua's circuit with a discontinuous nonlinearity[J].Journal of Circuits,Systems,and Computers,1993,3(1):231-237.
[18]SUYKENS J A K,VANDEWALLE J.Generation of n-double scrolls[J].Circuits and Systems I:Fundamental Theory and Applications,IEEE Transactions on,1993,40(11):861-867.
[19]YIN Y Z.Synchronization of chaos in a modified Chua’s circuit using continuous control[J].International Journal of Bifurcation and Chaos,1996,6(11):2101-2117.
[20]刘明华,禹思敏.多涡卷高阶广义Jerk电路[J].物理学报,2006,55(11):5707-5713.LIU M H,YU S M.Multi-scroll high-order general Jerk circuits[J].Acta Phys Sin,2006,55(11):5707-5713.
[21]李亚,禹思敏,戴青云.一种新的蔡氏电路设计方法与硬件实现[J].物理学报,2006,55(8):3938-3944.LI Y,YU S M,DAI Q Y.A novel approach for Chua’s circuit design and its hardware implementation[J].Acta Phys Sin,2006,55(8):3938-3944.
[22]SAKTHIVEL G,RAJASEKAR S,THAMILMARAN K.Statistical measures and diffusion dynamics in a modified Chua’s circuit equation with multi-scroll attractors[J].International Journal of Bifurcation and Chaos,2012,22(1):1250004.
[23]TANG K S,ZHONG G Q,CHEN G.Generation of n-scroll attractors via sine function[J].IEEE Trans.Circuits Syst-I,2001,48(11):1369-1372.
[24]PENG Z,WANG C,LUO X.A novel multi-directional multi-scroll chaotic system and its CCII+circuit implementation[J].Optik-International Journal for Light and Electron Optics,2014,125(22):6665-6671.
[25]WANG C,LUO X,WAN Z.Generation and circuit implementation of multi-block multi-directional grid multi-scroll chaotic attractors[J].Optic-International Journal for Light and Electron Optics,2014,125(22):6716-6721.
[26]毛学志,徐勇,刘建平.基于反正切的网格混沌吸引子及其保密通信[J].通信学报,2014,35(12):106-115.MAO X Z,XU Y,LIU J P.Grid chaotic attractors based on arc tangent and its secure communication[J].Journal on Communications,2014,35(12):106-115.
[27]于娜,丁群,陈红.异结构系统混沌同步及其在保密通信中的应用[J].通信学报,2007,28(10):73-78.YU N,DING Q,CHEN H.Synchronization of different structure chaotic systems and the application in secure communication[J].Journal on Communication,2007,28(10):73-78.
[28]MA Y,LI Y,JIANG X.Simulation and circuit implementation of12-scroll chaotic system[J].Chaos,Solitons&Fractals,2015,75:127-133.
[29]LI H,WANG L,DUAN S.A memristor-based scroll chaotic system-design,analysis and circuit implementation[J].International Journal of Bifurcation and Chaos,2014,24(07):1450099.
[30]孙克辉.混沌保密通信原理与技术[M].北京:清华大学出版社,2015:58-110.SUN K H.Principle and technology of chaotic secure communication[M].Beijing:Tsinghua University Press,2015:58-110.作者简介:马均澎(1991-),男,山西运城人,西南大学硕士生,主要研究方向为混沌电路设计、非线性系统控制。