CLC number: O415.5

Anti-Control of Hopf Bifurcation for a Chaotic System with Infinite Equilibria

一个具有无穷平衡点的混沌系统Hopf分岔反控制

College of Mechanical and Electrical Engineering, Wuhan Qingchuan University, Wuhan 430204, Hubei, China

Received: 13 November 2024

Abstract

One method to change the bifurcation characteristics of chaotic systems is anti-control, which can either delay or advance bifurcation and transform an unstable state into a stable one. The chaotic system with infinite equilibria exhibits complex bifurcation characteristics. The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed. An improved dynamic state feedback control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled. A hybrid controller that includes both nonlinear and linear controllers is set up for the system. With the method, the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved. Numerical analysis verified the correctness.

摘要

反控制是改变混沌系统分岔特性的方法之一，它可以使分岔延迟或提前,使不稳定状态变为稳定状态。具有无穷平衡点的混沌系统表现出复杂的分岔特性。本文分析了系统Hopf分岔特性和对称共存的隐藏吸引子。为了降低复杂的计算过程，采用了一种改进型动态反馈控制方法进行Hopf分岔分析，并为系统设置了一个包括非线性和线性控制器的混合控制器。利用该方法，研究了系统Hopf分岔的延迟和稳定性，实现了反控制的目的。数值分析验证了其正确性。