Sufficient conditions for inverse anticipating synchronization of unidirectional coupled chaotic systems with multiple time delays

In this paper, inverse anticipating synchronization of two unidirectional coupled chaotic systems with a single time delay, two characteristic time delays and multiple time delays are investigated in detail, in which a general time-delayed chaotic system can drive another system in such a way that the driven system anticipates the driver by synchronizing with its inverse future state. This form of chaos synchronization offers more opportunities for reducing the unpredictability of complex dynamics. Sufficient conditions for inverse anticipating synchronization are given via rigorously theoretical analysis based on the Krasovskii-Lyapunov functional method. Our main result contains some existing results as special cases, which had been widely used as a direct extension of a simple case firstly investigated by K. Pyragas without any theoretical proof. Numerical simulations further verified the rightness and effectiveness of our proposed method.