Construction and synchronization for a new time-delayed chaotic system

Three-dimensional chaotic systems produce only one positive Lyapunov exponent. While this structure is simple, it has the disadvantage of degraded secrecy performance. Chaotic systems presented in this paper on the basis of constructing a new time-delayed chaotic systems, due to the solution exists in infinite-dimensional spaces, the dynamic behavior of the new system compared with the original system becomes more complicated. Therefore on the basis of the guarantee system structure is relatively simple and then increased the confidentiality of the signal. Based on the theory of Lyapunov functionals, this paper build a suitable controller to realize the delay synchronization of chaotic systems. Based on Lyapunov-krasovskii functional, we propose a controller to prove in theory, through the Matlab software, the numerical simulation results demonstrate the feasibility of the algorithm.