Controlling hyperchaos of the Rossler system

Abstract

A feedback control is designed to regulate the hyperchaotic behaviour of the Rossler oscillator. Two inputs are added to the system for the control where each of the inputs contains two portions of feedback. One of the feedback parts is to construct an equilibrium manifold by modifying the dynamics of the system, while the other is the proportional feedback part which will control the hyperchaotic state to desired states on the manifold. In the design, the desired states include fixed points as well as limit cycles. Some numerical experiments are presented to perform the control. As expected, and also verified by the numerical results, the hyperchaotic system can be well tracked to the desired state by the present design. Furthermore, the settling times of the tracking can be improved by increasing the proportional gains of the control.