Destabilization and Route to Chaos in Neural Networks with Random Connectivity

The occurence 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. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function but independent of the connectivity, that allows a sustained activity and the occurence 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 quasi-periodic one, whatever the type of the first bifurcation is (Hopf bifurcation, pitchfork or flip).