有源荷控忆阻系统的多稳态分析及电路实现
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摘要
采用有源荷控忆阻替换蔡氏电路中的非线性电阻,实现一个五维忆阻非线性电路系统.建立了该系统的无量纲方程,分析了系统的平衡点集与稳定性.利用分岔图、Lyapunov指数谱和相轨迹图等分析方法,从多角度研究了随系统参数与初始状态变化而产生的多稳态动力学行为.研究表明,当系统参数、初始状态变化时,都会出现不同拓扑结构的混沌吸引子共存、不同吸引域的多周期极限环共存、不同周期数的极限环与不同拓扑结构的混沌吸引子等共存行为.最后,设计了五维忆阻混沌系统的模拟电路模型,电路仿真实验与数值仿真结果相一致,观测到不同的多稳态共存运动.这表明动力学分析的正确性和系统的物理可实现性,为进一步拓展系统加密应用奠定基础.
In the paper,a new type of five-dimensional memristive chaotic system is easily implemented by replacing a nonlinear resistance in the Chua's circuit with an active charge-controlled memristor. Firstly,the stable equilibrium and unstable equilibrium point sets of the system are analyzed theoretically by establishing the dimensionless equation. Next,through Lyapunov index spectrum,bifurcation diagram and phase track diagram,the coexistence phenomena of the system with respect to the changes and initial condition is studied. When different initial conditions are used,the system displays the coexistent phenomenon of chaotic attractors with different topological structures or several limit cycles with different attraction domains,as well as the phenomenon of multiple attractors of several periodic limit cycle and chaotic attractors with multiple topological structures. Finally,based on multisim circuit simulation model,the simulation results are consistent with the numerical simulations and relevant theoretical analysis. These show the correctness of dynamic analysis and the physical realizability of the system,and lay a foundation for expanding the application in encryption.
In the paper,a new type of five-dimensional memristive chaotic system is easily implemented by replacing a nonlinear resistance in the Chua's circuit with an active charge-controlled memristor. Firstly,the stable equilibrium and unstable equilibrium point sets of the system are analyzed theoretically by establishing the dimensionless equation. Next,through Lyapunov index spectrum,bifurcation diagram and phase track diagram,the coexistence phenomena of the system with respect to the changes and initial condition is studied. When different initial conditions are used,the system displays the coexistent phenomenon of chaotic attractors with different topological structures or several limit cycles with different attraction domains,as well as the phenomenon of multiple attractors of several periodic limit cycle and chaotic attractors with multiple topological structures. Finally,based on multisim circuit simulation model,the simulation results are consistent with the numerical simulations and relevant theoretical analysis. These show the correctness of dynamic analysis and the physical realizability of the system,and lay a foundation for expanding the application in encryption.
引文
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[17] LI Q D,ZENG H Z,LI J.Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria[J].Nonlinear dynamics,2015,79(4):2295-2308.
[18] DANG X Y,LI C B,BAO B C et al.Complex transient dynamics of hidden attractors in simple 4D system[J].Chinese physics B,2015,24(5):050503.
[2] STRUKOV D B,SNIDER G S,STEWART D R,et al.The missing memristor found[J].Nature,2008,453(7191):80-83.
[3] 武花干,包伯成,徐权.基于二极管桥与串联RL滤波器的一阶广义忆阻器[J].电子学报,2015,43(10):2192-2132.WU H G,BAO B C,XU Q.First order generalized memristor emulator based on diode bridge and series RL filter[J].Acta electronica sinica,2015,43(10):2129-2132.(in Chinese)
[4] 闵富红,王珠林,王恩荣,等.新型忆阻器混沌电路及其在图像加密中的应用[J].电子与信息学报,2016,38(10):2681-2688.MIN F H,WANG Z L,WANG E R,et al.New memristor chaotic and its application to encryption[J].Journal of electronics & information technology,2016,38(10):2681-2688.(in Chinese)
[5] 刘东青,程海峰,朱玄,等.忆阻器及其阻变机理研究进展[J].物理学报,2014,63(18):187301.LIU D Q,CHENG H F,ZHU X,et al.Research progress of memristors and memristive mechanism[J].Acta physica sinica,2014,63(18):187301.(in Chinese)
[6] 洪庆辉,曾以成,李志军.含磁控和荷控两种忆阻器的混沌电路设计与仿真[J].物理学报,2013,62(23):230502.HONG Q H,ZENG Y C,LI Z J.Design and simulation of chaotic circuit for flux-controlled memristor and charge-controlled memristor[J].Acta physica sinica,2013,62(23):230502.(in Chinese)
[7] 吴洁宁,王丽丹,段书凯.基于忆阻器的时滞混沌系统及伪随机序列发生器[J].物理学报,2017,66(3):030502.WU J N,WANG L D,DUAN S K.A memristor-based time-delay chaotic systems and paeudo-random sequence generater[J].Acta physica sinica,2017,66(3):030502.(in Chinese)
[8] YUAN F,WANG G Y,WANG X W.Extreme multistability in a memristor-based multi-scroll hyper-chaotic system[J].Chaos,2016,26(7):073107.
[9] PENG G Y,MIN F H.Multistability analysis,circuit implementations and application in image encryption of a novel memristive chaotic circuit[J].Nonlinear dynamics,2017,90(3):1607-1625.
[10] PATEL M S,PATEL U,SEN A,et al.Experimental observation of extreme multistability in an electronic system of two coupled R?ssler oscillators[J].Physical reviewe E,2014,89(2):022918.
[11] 俞清,包伯成,胡丰伟,等.基于一阶广义忆阻器的文氏桥混沌振荡器研究[J].物理学报,2014,63(24):240505.YU Q,BAO B C,HU F W,et al.Wien-bridge chaotic oscillator based on first-order generalized memristor[J].Acta physica sinica,2014,63(24):240505.(in Chinese)
[12] 包涵,包伯成,林毅,等.忆阻自激振荡系统的隐藏吸引子及其动力学特性[J].物理学报,2016,65(18):180501.BAO H,BAO B C,LIN Y,et al.Hidden attrctor and its dynamical characteristic in memristive self-oscillating system[J].Acta physica sinica,2016,65(18):180501.(in Chinese)
[13] SPROTT J C,LI C B.Comment on“How to obtain extreme multistability in coupled dynamical systems”[J].Physical reviewe E,2014,89(6):066901.
[14] 阮静雅,孙克辉,牟俊.基于忆阻器反馈的Lorenz超混沌系统及其电路实现[J].物理学报,2016,65(19),190502.RUAN J Y,SUN K H,MOU J.Memristor-based Lorenz hyper-chaotic system and its circuit implementation[J].Acta physica sinica,2016,65(19):190502.(in Chinese)
[15] XU Q,LIN Y,BAO B C,et al.Multiple attractors in a non-ideal active voltage-controlled memristor based Chua’s circuit[J].Chaos solitons and fractals,2016,83:186-200.
[16] KENGNE J,TABEKOUENG Z N,TAMBA V K,et al.Periodicity,chaos,and multiple attractors in a memristor-based Shinriki’s circuit[J].Chaos,2015,25(10):103126.
[17] LI Q D,ZENG H Z,LI J.Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria[J].Nonlinear dynamics,2015,79(4):2295-2308.
[18] DANG X Y,LI C B,BAO B C et al.Complex transient dynamics of hidden attractors in simple 4D system[J].Chinese physics B,2015,24(5):050503.