A new synchronization algorithm for delayed complex dynamical networks via adaptive control approach

An adaptive control strategy is developed for complex delayed dynamical networks with time-varying coupling strength and time-varying delayed. Using the Lyapunov stability theory, an adaptive control is designed to ensure the asymptotic convergence of the synchronization error, a sufficient condition of the synchronization is obtained. By constructing a Lyapunov–Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the error. An example of the complex network is finally used to verify the proposed theoretical result.