Controlling Chaos of a New Dynamical System with Feedback Control

Controlling chaos is a topic in nonlinear dynamics which attracted a great deal of work in the last twenty years. Even though there are more definitions of the chaos [4], a distinctive characteristic of the chaotic behavior of a dynamical system is its sensitive dependence on the initial conditions. Generally, chaos is believed to be harmful because in many cases it can lead to disasters. Chaotical behavior is observed in practical applications of many fields, from engineering to biology and economics. Chaos can be suppressed using linear or nonlinear feedback methods [1], [2], [3], [5], [6]. The present work is organized as follows. In Section 1 we record some basic details of the system under study. Section 2 describes the methods to control chaos to the unstable fixed points, while Section 3 presents a linear feedback control of the system. Numerical illustrations are presented in all the Sections.