Control of a simple chaotic flow having a line equilibrium by means of a single passive controller

Abstract

Recently, Jafari and Sprott (2013) have found nine simple chaotic flows with quadratic nonlinearities which include the unusual feature of having a line equilibrium. This study investigates the control of a simple chaotic system having a line equilibrium by means of the passive control method. Lyapunov function is used to realize that the passive controller ensures the global asymptotic stability of the system In order to validate all the theoretical analyses, numerical simulations are demonstrated. Owing to the single passive controller, the chaotic flow stabilizes towards its line equilibrium in the state space effectively.