Stability and synchronization of a fractional BAM neural network system of high-order type

TL;DR

This paper investigates the stability and synchronization of a high-order fractional BAM neural network with delays, employing fractional calculus and Laplace transform techniques to establish theoretical results validated by examples.

Contribution

It introduces a novel analysis framework for high-order fractional BAM neural networks with delays, including unbounded activation functions, using Mittag-Leffler stability and fractional Halanay inequality.

Findings

Established Mittag-Leffler stability criteria

Proved synchronization conditions for the network

Validated results with explicit examples

Abstract

In this paper, stability and synchronization of a Caputo fractional BAM neural network system of high-order type and neutral delays are examined. A mixture of properties of fractional calculus, Laplace transform, and analytical techniques is used to derive Mittag-Leffler stability and synchronization for two classes of activation functions. A fractional version of Halanay inequality is utilized to deal with the fractional character of the system and some suitable evaluations and handling to cope with the higher order feature. Another feature is the treatment of unbounded activation functions. Explicit examples to validate the theoretical outcomes are shown at the end.