Quasi-periodicity and bifurcation phenomena in Ising spin neural networks with asymmetric interactions
S. N. Laughton, A C C Coolen · Journal of Physics A Mathematical and General · 1994
The evolution of macroscopic order parameters in separable, stochastic neural networks, which becomes deterministic in the thermodynamic limit, can be completely described by the inverse 'temperature' beta , the embedding matrix A, and the set of initial conditions (m 0 ). Using mainly the techniques of bifurcation theory we present evidence that the qualitative behaviour is governed by one relevant eigenvalue of the matrix A. We show that a variety of bifurcation phenomena can occur as beta is varied, including quasi-periodic solutions displaying mode locking in the discrete time case. We illustrate our results with numerical simulations of, for reasons of computational intensity, the discrete time case only.