Analysis and adaptive synchronization for a new chaotic system

In this paper, a new three-dimensional autonomous chaotic system is presented. There are three control parameters and three different nonlinear terms in the governed equations. The new chaotic system has six equilibrium points. Basic dynamic properties of the new system are investigated via theoretical analysis and numerical simulation. The nonlinear characteristic of the new chaotic system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, a dissipative system, Poincar, maps and bifurcations. Then, an adaptive control law is derived to make the states of two identical chaotic systems asymptotically synchronized based on the Lyapunov stability theory. Finally, a numerical simulation is presented to verify the effectiveness of the proposed synchronization scheme.