Chaos in nervous system is a fascinating but controversial field of investigation. To approach the role of chaos in the real brain, we theoretically and numerically investigate the occurrence of chaos inartificial neural networks. Most of the time, recurrent networks (with feedbacks) are fully connected. This architecture being not biologically plausible, the occurrence of chaos 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, 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. The route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is. Our results suggest that such high-dimensional networks behave like low-dimensional dynamical systems. (shrink)

The dynamical behaviour of a very general model of neural networks with random asymmetric synaptic weights is investigated in the presence of random thresholds. Using mean-field equations, the bifurcations of the fixed points and the change of regime when varying control parameters are established. Different areas with various regimes are defined in the parameter space. Chaos arises generically by a quasi-periodicity route.

This paper is concerned with the modeling of neural systems regarded as information processing entities. I investigate the various dynamic regimes that are accessible in neural networks considered as nonlinear adaptive dynamic systems. The possibilities of obtaining steady, oscillatory or chaotic regimes are illustrated with different neural network models. Some aspects of the dependence of the dynamic regimes upon the synaptic couplings are examined. I emphasize the role that the various regimes may play to support information processing abilities. I present (...) an example where controlled transient evolutions in a neural network, are used to model the regulation of motor activities by the cerebellar cortex. (shrink)