The characteristics and self-time-delay synchronization of two-time-delay complex Lorenz system

Abstract Time-delay is frequently encountered in a variety of practical chaotic systems, such as chaos-communication. The behaviours of time-delay chaotic system are greatly different from those of the original system. Self-time-delay synchronization (STDS) implies that the synchronization between the time-delay system and the original system while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Firstly, we investigate the characteristics of two-time-delay complex Lorenz system. Then we take one-time-delay and two-time-delay complex Lorenz system as examples, and design their controllers to realize STDS. One-time-delay complex Lorenz system is a special case of two-time-delay. Numerical simulations verify the validity of the STDS controllers. The controllers only involve error, and it is easy to realize in practice. Moreover, the time-delay chaotic system exhibits highly stochastic behaviors and unpredictable properties, which can be applied to chaos-communication and enhance the security of communication.