Dual-anticipating, dual and dual-lag synchronization in modulated time-delayed systems

In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dual-anticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey-Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis.