Routes to Chaos in Neural Networks with Random Weights

D. J. Albers and J. C. Sprott
Department of Physics, University of Wisconsin, Madison,
1150 University Avenue, Madison, WI 53706, USA

 W. D. Dechert
Department of Economics, University of Houston,
Houston, TX 77204-5882, USA

(Received January 13, 1998; Revised May 9, 1998)


Neural networks are dense in the space of dynamical systems.  We present a Monte Carlo study of the dynamic properties along the route to chaos over random dynamical system function space by randomly sampling the neural network function space.  Our results show that as the dimension of the system (the number of dynamical variables) is increased, the probability of chaos approaches unity.  We present theoretical and numerical results which show that as the dimension is increased, the quasiperiodic route to chaos is the dominant route.  We also qualitatively analyze the dynamics along the route.

Ref: D. J. Albers, J. C. Sprott, and W. D. Dechert, International Journal of Bifurcation and Chaos 8, 1463-1478 (1998)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.