OGY Control of Haken Like Systems on Different Poincare Sections

TL;DR

This paper investigates the effectiveness of OGY control in stabilizing Haken-like chaotic systems, such as the Chua, Lorenz, Chen, and Lü systems, by analyzing different methods of defining their slow manifolds.

Contribution

It introduces and compares various approaches to defining slow manifolds in Haken-like systems to enhance OGY control efficiency.

Findings

Different slow manifold definitions impact control effectiveness.

OGY control successfully stabilizes chaotic Haken-like systems.

Method comparisons reveal optimal approaches for specific systems.

Abstract

The Chua system, the Lorenz system, the Chen system and The L\"u system are chaotic systems that their state space equations is very similar to Haken system which is a nonlinear model of a optical slow-fast system. These Haken-Like Sys-tems have very similar properties. All have two slow but unstable eigenvalues and one fastest but stable eigenvalue. This lets that an approximation of slow manifold be equivalent with unstable manifold of the system. In other hand, control of discreet model of the system on a defined manifold (Poincare map) is main essence of some important control methods of chaotic systems for example OGY method. Here, by using different methods of defining slow manifold of the H-L systems the efficiency of the OGY control for stabilizing problem investigated.