Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

•A new memristor-based BAM neural network system is formulated.•We analyze the viability and dissipativity of functional differential inclusions’ solutions.•We present a new method to obtain the existence of positive periodic solutions.•We utilize the theory of set-valued maps.•The functional differential inclusions of Filippov type are employed.

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.