Human perception is a complex nonlinear dynamics. On one hand it is periodic and on the other hand it is chaotic. Thus, we propose a hybrid model-the spatial chaotic dynamics for the associative recall to retrieve patterns, similar to Walter Freeman's discovery, and the fixed point dynamics for memory storage, similar to Hopfield and Grossberg's findings. Each neuron in the network is a chaotic map, whose phase space is divided into two states. One is periodic dynamic state of period V, representing a V-value retrieved pattern; another is chaotic dynamic state corresponding to searching process. Firstly, patterns are stored in memory by the pseudo-inverse matrix learning algorithm. In the retrieving process, all neurons are initially set to be chaotic. Due to the ergodicity property of chaos, each neuron will approximate the periodic points covered by the chaotic attractor at some instants. When this occurs, the control is activated to drive the dynamics of each neuron to one of the V stable periodic points. If a neuron is driven to a wrong periodic point, it contributes to high partial energies to itself and all other neurons. As a consequence, some neurons may jump back to the chaotic state and the searching process continues until all neurons settle down at their correct periodic points. In this way, the corresponding stored pattern is retrieved. Computer simulations confirm the theoretical prediction.
Nota bibliográficaFunding Information:
The works of the first and the third author are funded in part by FAPESP under contract number Proc. 02/10707-0, Proc. 05/50697-1 and Proc. 04/12408-5.