Synchronization of Time-Varying Memristive Systems With Reaction-Diffusion via Time Delay Linear Feedback

In this paper, a new approach was proposed for the asymptotic and exponential synchronization of delayed memristive neural networks (MNNs) with time delay linear feedback. First, nonlinear MNNs with time-varying delay and reaction-diffusion effects are introduced under a partial differential equation. Then, utilizing an adaptive time delay controller with two terms consisting of the state and the state time delay, sufficient conditions are obtained for the asymptotical and exponential synchronization. The controller is independent of MNNs dynamic parameters and just is a function of error synchronization. The new Lyapunov functional stability was proposed in such a way that synchronization feasibility and damping characteristics improved and synchronization error decreased. Two algebraic inequalities are derived as straightforward and adequate conditions, which can ensure synchronization's objectives. The obtained conditions for synchronization with this approach are less dependent on the exact values of the system's dynamic parameters rather than previously known results. The efficiency of the proposed adaptive time-delay controller is verified by numerical simulations.