一个具有隐藏与共存吸引子的忆感器混沌系统
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摘要
在磁控忆感器数学模型的基础上,提出了一个新型四维连续混沌系统,通过分析系统的李雅普诺夫指数、分岔图和Poincaré截面等基本动力学特性,验证了系统的混沌特性。随着参数的变化,新系统可产生逆倍周期分岔现象,在系统参数固定不变而初始条件变化时,系统出现共存吸引子,并在特定条件下,出现隐藏吸引子。仿真实验表明:系统出现的混沌现象与理论分析结果一致。
A new four-dimensional continuous chaotic system is proposed, which is based on the mathematical model of meminductor. The chaotic characteristics of the system are verified by analyzing the basic dynamics including Lyapunov exponent, bifurcation diagram and Poincaré section. The proposed new system can generate the inverse period bifurcation phenomenon by changing the parameters. When the system parameters are fixed, coexisting attractors can appear under different initial conditions, while hidden attractors appear only under certain conditions. Simulation experiments show that the chaotic phenomena appearing in the system are consistent with the theoretical analysis results.
A new four-dimensional continuous chaotic system is proposed, which is based on the mathematical model of meminductor. The chaotic characteristics of the system are verified by analyzing the basic dynamics including Lyapunov exponent, bifurcation diagram and Poincaré section. The proposed new system can generate the inverse period bifurcation phenomenon by changing the parameters. When the system parameters are fixed, coexisting attractors can appear under different initial conditions, while hidden attractors appear only under certain conditions. Simulation experiments show that the chaotic phenomena appearing in the system are consistent with the theoretical analysis results.
引文
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[12] 袁方,王光义,靳培培.一种忆感器模型及其振荡器的动力学特性研究[J].物理学报,2015,64(21):214-226.
[2] LI T Y,YORKE J A.Period three implies chaos[J].The American Mathematical Monthly,1975,82(10):985-992.
[3] 李春来,禹思敏.一个新的超混沌系统及其自适应追踪控制[J].物理学报,2012,61(4):40504.
[4] 赵益波,张秀再,孙心宇.基于Weiner模型超混沌lü系统的自适应辨识[J].物理学报,2014,63(13):43-48.
[5] LI C,SPROTT J C,THIO W.Bistability in a hyperchaotic system with a line equilibrium[J].Journal of Experimental and Theoretical Physics,2014,118(3):494-500.
[6] LI C,SPROTT J C,THIO W,et al.A new piecewise linear hyperchaotic circuit[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2014,61(12):977-981.
[7] 胡串,李志军,陈茜茜.负参数空间分数阶Chua系统的动力学行为及实验验证[J].物理学报,2017,66(23):60-69.
[8] 孙克辉,杨静利,丘水生.分数阶混沌系统的电路仿真与实现[J].计算机仿真,2011,28(2):117-119.
[9] FOUDA M E,RADWAN A G.Meminductor response under periodic current excitations[J].Circuits,Systems,and Signal Processing,2014,33(5):1573-1583.
[10] SAH M P,BUDHATHOKI R K,YANG C,et al.Mutator-based meminductor emulator for circuit applications[J].Circuits,Systems,and Signal Processing,2014,33(8):2363-2383.
[11] SAH M P,BUDHATHOKI R K,YANG C,et al.Charge controlled meminductor emulator[J].Journal of Semiconductor Technology and Science,2014,14(6):750-754.
[12] 袁方,王光义,靳培培.一种忆感器模型及其振荡器的动力学特性研究[J].物理学报,2015,64(21):214-226.