Chaotic associative recalls for fixed point attractor patterns

Abstract

Human perception is a complex nonlinear dynamics. On the one hand it is periodic dynamics and on the other hand it is chaotic. Thus, we wish to propose a hybrid-the spatial chaotic dynamics for the associative recall to retrieve patterns, similar to Walter Freeman's discovery, and the fixed point dynamics for memory stage, similar to Hopfield and Grossberg's discoveries. In this model, each neuron in the network could be a chaotic map, whose phase space is divided into two states: one is periodic dynamic state with period-V, which is used to represent a V-value retrieved pattern; another is chaotic dynamic state. Firstly, patters are stored in the memory by fixed point learning algorithm. In the retrieving process, all neurons are initially set in the chaotic region. Due to the ergodicity property of chaos, each neuron will approximate the periodic points covered by the chaotic attractor at same instants. When this occurs, the control is activated to drive the dynamic of each neuron to their corresponding stable periodic point. Computer simulations confirm the theoretical prediction.