Mathematics

CLC number: O193

Chaotic Analysis and Control of a Two-Peak Discrete Chaotic System

一个双峰离散混沌系统的混沌分析和控制

¹ School of Intelligent Manufacturing, Jianghan University, Wuhan 430056, Hubei, China
² College of Mechanical and Electrical Engineering, Wuhan Qingchuan University, Wuhan 430204, Hubei, China

Received: 11 May 2024

Abstract

The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied. Through the study of the nonlinear dynamic behavior of the system, it is found that with the change of the system parameters, the system starts from a chaotic state, and then goes through intermittent chaos, stable region, period-doubling bifurcation to a chaotic state again. The system's critical conditions and process to generate intermittent chaos are analyzed. The feedback control method sets linear and nonlinear controllers for the system to control the chaos. By adjusting the value of control parameters, the intermittent chaos can be delayed or disappear, and the stability region and period-doubling bifurcation process of the system can be expanded. Both linear controllers and nonlinear controllers have the same control effect. The numerical simulation analysis verifies the correctness of the theoretical analysis.

摘要

本文研究了一个双峰离散混沌系统的非线性动力学特性。通过对系统非线性动力学行为的研究，发现随着系统参数的变化，系统从混沌状态开始，然后经历阵发混沌、稳定状态、倍周期分岔，再次进入混沌状态。分析了系统产生阵发混沌的临界条件和过程。反馈控制方法用于为系统设置线性控制器和非线性控制器来控制混沌。通过调整控制参数的值，可以延迟或消除阵发混沌，扩展系统的稳定区域和倍周期分岔过程。线性控制器和非线性控制器具有相同的控制效果。数值模拟分析验证了理论分析的正确性。