Approximation and decomposition of attractors of a Hopfield neural network system

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.