Chaos Synchronization of Chemical Models

Chaos synchronization of identical chemical reactors with different initial conditions is investigated by two approaches: linear coupling and a novel coupling which is proposed for the first time. Both approaches are studied under bidirectional and unidirectional schemes. The conditions to achieve stability of synchronization are determined by the Lyapunov theorem for linear coupling method. Also, stability condition is obtained when novel coupling is applied. In each section, numerical simulations are presented to verify the theoretical results. There are many control techniques to determine coupling terms such that error dynamics converges to zero. A general one is based on negative linear feedback of error dynamics. Moreover there are many nonlinear feedback based synchronization techniques where the coupling terms are nonlinear functions of error dynamics In this paper we use two schemes for coupling: first we start by linear coupling scheme in both bidirectional and unidirectional ways. We prove the stability of error dynamics by the Lyapunov theorem (Slotine & Li, 1991). Then we propose a novel method to couple both unidirectional and bidirectional for synchronization of two identical chaotic chemical reactors. We show that our coupling scheme can synchronize the considered system effectively and in a short time. Also, we study asymptotic stability of error dynamics theoretically. The rest of the paper is organized as follows: Next section is devoted to a brief introduction on synchronization problem. In section 3 the model of a well known chemical reactor is brought in. The chaotic behavior of this model has been studied in (Haung, 2005). Section 4 presents the synchronization problem with linear coupling in unidirectional and bidirectional schemes. In section 5, first the stability of synchronization by a new coupling scheme is shown by simulation. Then validity of the proposed method is revealed by the stability theory. The final section is dedicated to compare the linear coupling and the novel coupling schemes and weakness and advantages of these methods are studied.