四翼混沌系统及其Hopf分岔控制

1)沈阳化工大学信息工程学院,辽宁沈阳 110142; 2)工业环境-资源协同控制与优化技术辽宁省高校重点实验室,沈阳化工大学,辽宁沈阳 110142

系统学; 四翼混沌系统; Hopf分岔; 分岔控制; 极限环; 非线性系统; 保密通信

Four-wing chaotic system and its Hopf bifurcation control
YAN Minxiu1, 2 and XU Hui1

1)College of Information Engineering, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning Province, P.R.China2)Key Laboratory for Industrial Environment-Resources Cooperative Control and Optimization Technology, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning Province, P.R.China

systematics; four-wing chaotic system; Hopf bifurcation; bifurcation control; limit cycle; nonlinear system; secure communication

DOI: 10.3724/SP.J.1249.2021.02180

备注

为满足Hopf分岔控制的实际需要和通信保密对复杂混沌系统的需求,设计一个四翼混沌吸引子和基于washout滤波器的分岔控制器.基于Lorenz系统构建新的四翼系统,通过分岔图、李雅普诺夫指数和吸引子仿真分析系统的动力学演化,确定其混沌特性.基于高维Hopf分岔理论分析系统Hopf分岔的存在性,设计了一个基于washout滤波器,由线性项和非线性项组成的Hopf分岔控制器.该控制器在不改变系统平衡点的情况下,可实现系统在预期位置产生Hopf分岔,完成对极限环幅值和稳定性的控制.仿真结果表明,极限环幅值和分岔参数的临界值是可以控制的,验证了控制器的合理性和有效性.该研究拓展了混沌系统Hopf分岔控制的多样性,在通信和图像加密领域有潜在的应用.

In order to meet the practical needs of Hopf bifurcation control and communication security, we propose a four-wing chaotic attractor and a bifurcation controller based on washout filter. We analyze the dynamic evolution of system by means of bifurcation diagram, Lyapunov exponent and attractor simulation to determine its chaotic characteristics. Based on the high-dimensional bifurcation theory, we discuss the existence of Hopf bifurcation, and design a Hopf bifurcation controller based on washout filter, which is composed of linear and nonlinear terms. Without changing the equilibrium point of system, the controller can generate the Hopf bifurcation of system at the expected position, and realize the control of amplitude and stability of the limit cycle. The simulation results show that the amplitude of the limit cycle and the critical value of bifurcation parameters can be controlled, which verifies the rationality and effectiveness of the controller. This study expands the diversity of Hopf bifurcation control in chaotic system and has potential applications in communication and image encryption.

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