Approximation and decomposition of attractors of a Hopfield neural network system
Marius‐F. Danca, Guanrong Chen · Chaos Solitons & Fractals · 2024
In this paper, the Parameter Switching (PS) algorithm is used to numerically approximate attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating the 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. • Attractor decomposition as a convex combination of other attractors. • The Parameter Switching algorithm to approximate attractors. • Attractors of a HNN system are expressed as a convex combination of his attractors.