Approximation and decomposition of attractors of a Hopfield neural network system

TL;DR

This paper applies the Parameter Switching algorithm to approximate and decompose attractors in Hopfield neural networks, enabling new ways to analyze and potentially control chaos in such systems.

Contribution

It introduces the use of the Parameter Switching algorithm for attractor approximation and decomposition in Hopfield neural networks, a novel application in this context.

Findings

Every attractor can be expressed as a convex combination of others.

The PS algorithm effectively approximates attractors of the HNN system.

Potential for using PS as a control or anticontrol method for chaos.

Abstract

In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos.