Complex function projective synchronization in drive-response complex-variable dynamical networks with coupling time delays

This paper investigates complex function projective synchronization (CFPS) in drive-response complex-variable dynamical networks, which means that the complex-variable chaotic systems in networks may evolve in different directions with a time-varying intersection angle in a complex plane and can be synchronized up to a complex scaling function. Hybrid feedback control schemes are proposed to achieve CFPS in drive-response complex-variable networks with both constant coupling delay and time-varying coupling delay. Based on Lyapunov stability theory and the linear matrix inequality, some sufficient conditions are derived by adopting an appropriate Lyapunov-krasovskii energy function. Finally, the numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method and further reveal that the synchronization is independent of the coupling delay.