International Journal of Bifurcations and Chaos, 1996, vol. 6, No. 4, pp. 627-646.
1-D Maps, Chaos and Neural
Networks For Information Processing
Yu. V. Andreyev, A.S. Dmitriev and D.A. Kuminov
Institute of Radioengineering and Electronics of the
Russian Academy of Sciences
Moscow, 103907, Russia
L. 0. Chua and C. W. Wu
Electronics Research Laboratory and
Department of Electrical Engineering and Computer Sciences,
University of California, Berkeley, CA 94720, USA
International Journal of Bifurcations and Chaos,
1996, vol. 6, No. 4, pp. 627-646.
Received February 15, 1993. Revised December 28, 1995
and October 3, 1995.
An application of complex dynamics and chaos in neural networks to information processing is studied. Mathematical models based on piecewise-linear maps implementing basic functions of information processing via complex dynamics and chaos are discussed. Realizations of these models by neural networks are presented. In contrast to other methods of using neural networks
and associative memory to store information, the information is stored in dynamical attractors such as limit cycles, rather than equilibrium points. Retrieval of information corresponds to getting the state into the basin of attraction of the attractor. We show that noise-corrupted information or partial information are sufficient to drive the state into the basin of attraction of the attractor, thus these systems exhibit the property of associative memory.