CONTROL OF THE TRANSITION TO CHAOS IN NEURAL NETWORKS WITH RANDOM CONNECTIVITY

Abstract

The occurrence of chaos in recurrent neural networks is supposed to depend on the architecture and on the synaptic coupling strength. It is studied here for a randomly diluted architecture. We produce a bifurcation parameter independent of the connectivity that allows a sustained activity and the occurrence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. Moreover the route towards chaos is numerically checked to be a quasiperiodic one, whatever the type of the first bifurcation is. In the discussion, we connect these results to some recent theoretical results about highly diluted networks. Hints are provided for further investigations to elicit the role of chaotic dynamics in the cognitive processes of the brain.