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一个新隐藏多稳态混沌系统的分析及仿真实现

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在Shimizu-Morioka系统中引入变量w,构造一个新的四维混沌系统.该系统在参数不同时可产生无平衡点的隐藏吸引子和具有不稳定鞍点的自激吸引子.通过分析系统的吸引子相图、分岔图等基本动力学特性,并计算李雅普诺夫指数谱和复杂度等发现,随着参数的变化,系统产生倍周期、逆倍周期分岔和吸引子形态的变化.在系统参数不变,初始条件改变时,系统出现多种类型的共存吸引子,如同类型周期吸引子共存、不同类型周期吸引子共存、单翼混沌吸引共存、双翼混沌吸引子共存、不同类型混沌吸引子共存以及周期吸引子和混沌吸引子共存,从而产生多稳态现象.最后采用Multisim软件对混沌系统进行模拟电路的实现.
Analysis and simulation implementation of a new chaotic system with hidden multistability
Constructing a new four-dimensional chaotic system by introducing the variable w in the Shimizu-Morioka system.The system can produce hidden attractors without equilibrium points and self-excited attractors with unstable saddle points when the parameters are different.By analysing the basic dynamical properties of the system such as attractor phase diagrams and bifurcation di-agrams,and calculating the Lyapunov exponential spectrum and complexity,it is found that the system produces period-doubling,period-doubling reversals and changes in attractor morphology as the parameters are varied.When the parameters of the system are fixed and the initial conditions are changed,the system appears to have many types of coexisting attractors.These include coexistence of same type of periodic attractors,coexistence of different types of periodic attractors,coexistence of single-winged chaotic attract-ors,coexistence of double-winged chaotic attractors,coexistence of different types of chaotic attractors,and coexistence of periodic attractors and chaotic attractors.Thus the system generates the phenomenon of multistability.Finally,the implementation of the simu-lation circuit for the chaotic system is carried out using Multisim software.

chaotic systemshidden attractormultistabilitycircuit simulation

李贤丽、张丽敏、梁武燕、杨忠宝、李静静、于婷婷

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东北石油大学物理与电子工程学院,黑龙江大庆 163318

混沌系统 隐藏吸引子 多稳态 电路仿真

2024

自动化与仪器仪表
重庆工业自动化仪表研究所,重庆市自动化与仪器仪表学会

自动化与仪器仪表

CSTPCD
影响因子:0.327
ISSN:1001-9227
年,卷(期):2024.(6)
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