Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuli

TL;DR

This paper studies the convergence and invariant regions of general neural networks with almost periodic stimuli, establishing conditions for exponential convergence to multiple almost periodic patterns.

Contribution

It introduces new criteria for convergence and invariant regions in neural networks with almost periodic inputs, extending previous results in the field.

Findings

Established invariant regions for $2^N$ almost periodic patterns.

Derived criteria for exponential convergence to these patterns.

Extended and generalized previous theoretical results.

Abstract

In this paper, we investigate convergence dynamics of $2^N$ almost periodic encoded patterns of general neural networks (GNNs) subjected to external almost periodic stimuli, including almost periodic delays. Invariant regions are established for the existence of $2^N$ almost periodic encoded patterns under two classes of activation functions. By employing the property of $\mathscr{M}$-cone and inequality technique, attracting basins are estimated and some criteria are derived for the networks to converge exponentially toward $2^N$ almost periodic encoded patterns. The obtained results are new, they extend and generalize the corresponding results existing in previous literature.