四翼超混沌系统的动力学特性分析及其电路实现
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摘要
为了提高混沌系统的复杂性,本文基于最新提出的简化Lorenz系统,采用正弦函数扰动方法和非奇异变换,设计了一个具有四翼吸引子结构的超混沌系统。通过计算Lyapunov指数、分岔图、相图和Poincaré截面等方法分析了该系统的动力学特性,分析表明该系统具有丰富的动力学行为。采用分立元件,设计了该系统的模拟电路,电路实验结果与数值仿真结果相吻合,为构建具有高性能的混沌保密通信系统奠定了基础。
To improve the complexity of a chaotic system,a sinusoidal forcing function and a nonsingular transformation are applied to generate hyperchaotic system with four wings structure based on the simplified Lorenz system in this paper.Dynamics of the hyperchaotic and four-wing attractor system are analyzed and verified by means of Lyapunov exponent spectrums,bifurcation diagrams,phase portraits and Poincaré sections.Results of numerical analysis and simulations show the four-wing hyperchaotic system has complex dynamical behaviors.An electronic circuit of the four-wing hyperchaotic system is designed and experimented with discrete components.Circuit experiment results are agreed well with the simulation results,and it lays a good foundation for designing chaotic secure communication with high performances.
To improve the complexity of a chaotic system,a sinusoidal forcing function and a nonsingular transformation are applied to generate hyperchaotic system with four wings structure based on the simplified Lorenz system in this paper.Dynamics of the hyperchaotic and four-wing attractor system are analyzed and verified by means of Lyapunov exponent spectrums,bifurcation diagrams,phase portraits and Poincaré sections.Results of numerical analysis and simulations show the four-wing hyperchaotic system has complex dynamical behaviors.An electronic circuit of the four-wing hyperchaotic system is designed and experimented with discrete components.Circuit experiment results are agreed well with the simulation results,and it lays a good foundation for designing chaotic secure communication with high performances.
引文
[1]Thamilmaran K,Lakshmanan M,Venkatesan A.Hyperchaos in a modified canonical Chua’s circuit[J].International Journal of Bifurcationand Chaos,2004,14(l):221-243.
[2]Cafagna D,Grassi G.New 3D-scroll attractors in hyperchaotic Chua’s circuits forming a ring[J].International Journal of Bifurcation andChaos,2003,13(10):2889-2903.
[3]郑皓洲,胡进峰,徐威,刘立东,何子述.一类新型超混沌系统的非线性反馈同步研究[J].电子与信息学报,2011,33(4):844-848.
[4]胡英辉,郑远,邓云凯.超混沌调相信号抗干扰技术研究[J].电子与信息学报,2008,30(7):1756-1759.
[5]Tamasevicius A,Namajunas A,Cenys A.Simple 4D chaotic oscillator[J].Electronics Letters,1996,32(11):957-958.
[6]Yang Xiao-song,Li Qing-du,Chen Guan-rong.A twin-star hyperchaotic attractor and its circuit implementation[J].International Journal ofCircuit Theory and Applications,2003,31(6):637-640.
[7]Takahashi Y,Nakano H,Saito T.A simple hyperchaos generator based on impulsive switching[J].IEEE Transactions on Circuits andSystemsⅡ,2004,51(9):468-472.
[8]Zheng Song,Dong Gao-gao,Bi Qin-sheng.A new hyperchaotic system and its synchronization[J].Applied Mathematics and Computation,2010,215(9):3192-3200.
[9]Niu Yu-jun,Wang Xing-yuan,Wang Ming-jun,Zhang Hua-guang.A new hyperchaotic system and its circuit implementation[J].CommunNonlinear Sci Numer Simulat,2010,15(11):3518-3524.
[10]Sun Mei,Tian Li-xin,Zeng Chang-yan.The energy resources system with parametric perturbations and its hyperchaos control[J].NonlinearAnalysis:Real World Applications,2009,10(4):2620-2626.
[11]Sun Ke-hui,Sprott J C.Periodically forced chaotic system with signum nonlinearity[J].International Journal of Bifurcation and Chaos,2010,20(5):1499-1507.
[12]Bao Bo-cheng,Xu Qiang,Xu Jian-ping.Multi-scroll hyperchaotic system based on Colpitts model and its circuit implementation[J].Journalof Electronics,2010,27(4):538-543
[13]陈仕必,曾以成,徐茂林,陈家胜.用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现[J].物理学报,2011,60(2):551-557.
[14]包伯成,刘中,许建平,朱雷.基于Colpitts振荡器模型生成的多涡卷超混沌吸引子[J].物理学报,2010,59(3):1540-1548.
[15]禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J].物理学报,2003,52(1):25-33.
[16]王发强,刘崇新,逯俊杰.四维系统中多涡卷混沌吸引子的仿真研究[J].物理学报,2006,55(7):3289-3294.
[17]胡国四.一类具有四翼吸引子的超混沌系统[J].物理学报,2009,58(6):3734-3741.
[18]Sun Ke-hui,Sprott J.C.Dynamics of a simplified Lorenz system[J].International Journal of Bifurcation and Chaos,2009,19(4):1357-1366.
[19]Vaněek A,elikovsky S.Control systems:From linear analysis to synthesis of chaos[M].London:Prentice-Hall,1996.
[2]Cafagna D,Grassi G.New 3D-scroll attractors in hyperchaotic Chua’s circuits forming a ring[J].International Journal of Bifurcation andChaos,2003,13(10):2889-2903.
[3]郑皓洲,胡进峰,徐威,刘立东,何子述.一类新型超混沌系统的非线性反馈同步研究[J].电子与信息学报,2011,33(4):844-848.
[4]胡英辉,郑远,邓云凯.超混沌调相信号抗干扰技术研究[J].电子与信息学报,2008,30(7):1756-1759.
[5]Tamasevicius A,Namajunas A,Cenys A.Simple 4D chaotic oscillator[J].Electronics Letters,1996,32(11):957-958.
[6]Yang Xiao-song,Li Qing-du,Chen Guan-rong.A twin-star hyperchaotic attractor and its circuit implementation[J].International Journal ofCircuit Theory and Applications,2003,31(6):637-640.
[7]Takahashi Y,Nakano H,Saito T.A simple hyperchaos generator based on impulsive switching[J].IEEE Transactions on Circuits andSystemsⅡ,2004,51(9):468-472.
[8]Zheng Song,Dong Gao-gao,Bi Qin-sheng.A new hyperchaotic system and its synchronization[J].Applied Mathematics and Computation,2010,215(9):3192-3200.
[9]Niu Yu-jun,Wang Xing-yuan,Wang Ming-jun,Zhang Hua-guang.A new hyperchaotic system and its circuit implementation[J].CommunNonlinear Sci Numer Simulat,2010,15(11):3518-3524.
[10]Sun Mei,Tian Li-xin,Zeng Chang-yan.The energy resources system with parametric perturbations and its hyperchaos control[J].NonlinearAnalysis:Real World Applications,2009,10(4):2620-2626.
[11]Sun Ke-hui,Sprott J C.Periodically forced chaotic system with signum nonlinearity[J].International Journal of Bifurcation and Chaos,2010,20(5):1499-1507.
[12]Bao Bo-cheng,Xu Qiang,Xu Jian-ping.Multi-scroll hyperchaotic system based on Colpitts model and its circuit implementation[J].Journalof Electronics,2010,27(4):538-543
[13]陈仕必,曾以成,徐茂林,陈家胜.用多项式和阶跃函数构造网格多涡卷混沌吸引子及其电路实现[J].物理学报,2011,60(2):551-557.
[14]包伯成,刘中,许建平,朱雷.基于Colpitts振荡器模型生成的多涡卷超混沌吸引子[J].物理学报,2010,59(3):1540-1548.
[15]禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J].物理学报,2003,52(1):25-33.
[16]王发强,刘崇新,逯俊杰.四维系统中多涡卷混沌吸引子的仿真研究[J].物理学报,2006,55(7):3289-3294.
[17]胡国四.一类具有四翼吸引子的超混沌系统[J].物理学报,2009,58(6):3734-3741.
[18]Sun Ke-hui,Sprott J.C.Dynamics of a simplified Lorenz system[J].International Journal of Bifurcation and Chaos,2009,19(4):1357-1366.
[19]Vaněek A,elikovsky S.Control systems:From linear analysis to synthesis of chaos[M].London:Prentice-Hall,1996.