Emergence of Complexity in the Dynamic of a Diluted Neural Network

Abstract

Sensitive dependance on initial conditons is studied for a diluted and non symmetric model of neural networks. Two parameters appear to be relevant: the connectivity which allows local difference to spread all over the network and the noise temperature which smooths these difference. Their influence is shown by theoretical estimations in the thermodynamic limit and by simulations which give exactly the same results for medium size networks: when the connectivity reaches a critical threshold, transition from a “sensitive” dynamic to a single attractor dynamic is exhibited for a critical temperature which can be computed. This result is proved first for constant connectivity models then for randomly diluted models.