Chaotic Synchronization Of Three Coupled Lorenz-type Systems With A Ring Connection

Chaos, as an important part of nonlinear science, has abstracted more and more attention of scientists in different field. Control and synchronization of chaos systems has got much progress, motivating the strong passion of human being to rein chaos, which stands at the status betweens stochastic and deterministic. In this paper, we firstly make some qualitative analysis to Lorenz critical chaotic system, and then lead it to the corresponding unstable equilibrium point and periodic orbits in terms of the linear state feedback approach. Then we make a lot of simulations which indicate this method to be feasible. Fractional-order system, as well as Lyapunov exponent, has been used as a powerful tool for the quantitative study of chaotic systems. At the latter part of this paper, we use the approach of fractional-order calculus and Laplace transformation to study the synchronization among three identical chaotic systems with ring connection, which have various ways of coupling (unidirectional or bidirectional). And also, we make a preliminary work about the influence, the parameters of coupling to the rate of speed of synchronization. Finally, many numeric simulations are given to verify the effectiveness of the corresponding method.