Global exponential almost periodicity of a delayed memristor-based neural networks

• Use the Filippov solution to study the dynamics of delayed memristor-based neural networks.
• Prove the existence and uniqueness of almost periodic solution of the neural network under some conditions.
• Obtain the global exponential stability of the almost periodic solution.
• Prove the existence and stability of periodic solution of delayed neural networks with periodic memristor.

In this paper, the existence, uniqueness and stability of almost periodic solution for a class of delayed memristor-based neural networks are studied. By using a new Lyapunov function method, the neural network that has a unique almost periodic solution, which is globally exponentially stable is proved. Moreover, the obtained conclusion on the almost periodic solution is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed memristor-based neural networks with periodic coefficients (or constant coefficients). The obtained results are helpful to design the global exponential stability of almost periodic oscillatory memristor-based neural networks. Three numerical examples and simulations are also given to show the feasibility of our results.