ALMOST ANTI-PERIODIC FUNCTIONS AND THEIR APPLICATIONS ON A CLASS OF HOPFIELD NEURAL NETWORKS
This paper is devoted to investigating the existence of almost anti-periodic solutions of a class of neutral Hopfield neural networks with mixed delays.Firstly,the relationship between almost periodic function and almost anti-periodic functions is discussed,and it is proved that the set of all almost anti-periodic functions is a closed subspace of the almost periodic function space.Finally,by using the fixed point principle,it is proved that the Hopfield neural network has a unique bounded solution,which is an almost anti-periodic function.Since the almost anti-periodic function is more precise than the almost periodic function,the discussion on the existence and uniqueness of the almost anti-periodic solution of neural networks can more accurately describe the dynamic properties of neural networks than the discussion on the existence and uniqueness of the almost periodic solution,the obtained conclusion is novel and serves as a further refinement and supplement to existing conclusions.
Hopfield neural networksalmost periodic functionsalmost anti-periodic functionsBanach spacefixed point principle