Finite-time complete periodic synchronization of memristive neural networks with mixed delays

In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand side. In addition, some assumptions are determined to guarantee the globally exponentially stability of the solution. Then, we study the adaptive finite-time complete periodic synchronization problem and by applying Lyapunov-Krasovskii functional approach, a new adaptive controller and adaptive update rule have been developed. A useful finite-time complete synchronization condition is established in terms of linear matrix inequalities. Finally, an illustrative simulation is given to substantiate the main results.