Oscillations and chaos in neural networks: an exactly solvable model.
We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics.
Wang
L P
LP
Department of Chemistry, Stanford University, CA 94305.
Pichler
E E
EE
Ross
J
J
D000818:Animals; D001245:Association Learning; D008433:Mathematics; D008568:Memory; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*