Oscillatory and chaotic dynamics in neural networks under varying operating conditions

This paper studies the effects of a time-dependent operating environment on the dynamics of a neural network. In the previous paper Wang et al. (1990) studied an exactly solvable model of a higher order neural network. We identified a bifurcation parameter for the system, i.e., the rescaled noise level, which represents the combined effects of incomplete connectivity, interference among stored patterns, and additional stochastic noise. When this bifurcation parameter assumes different but static (time-independent) values, the network shows a spectrum of dynamics ranging from fixed points, to oscillations, to chaos. This paper shows that varying operating conditions described by the time-dependence of the rescaled noise level give rise to many more interesting dynamical behaviours, such as disappearances of fixed points and transitions between periodic oscillations and deterministic chaos. These results suggest that a varying environment, such as the one studied in the present model, may be used to facilitate memory retrieval if dynamic states are used for information storage in a neural network.