Almost periodic solutions of memristive multidirectional associative memory neural networks with mixed time delays

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains. In this paper, the memristive multidirectional associative memory neural networks (MAMNNs) with mixed time-varying delays are investigated in the sense of Filippov solution. First, three steps are given to prove the existence of the almost periodic solution. Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function. Second, the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function. The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions, Halanay inequality and Lyapunov function. The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks. Finally, numerical examples with simulations are presented to show the validity of the main results.

Automated summary

This paper investigates the memristive multidirectional associative memory neural networks (MAMNNs) with mixed time-varying delays in modeling the abrupt synaptic connections in human brain's associative memory. It proves the existence, boundedness, and asymptotical almost periodicity of the solution using Lyapunov function. It also examines the uniqueness and global exponential stability of the almost periodic solution using a new Lyapunov function. The research extends the study on the periodic and almost periodic solutions of bidirectional associative memory neural networks. Numerical examples and simulations are provided to demonstrate the validity of the main results.