As models of living beings acting in a real world biorobots undergo an accelerated “philogenic” complexification. The first efficient robots performed simple animal behaviours (e.g., those of ants, crickets) and later on isolated elementary behaviours of complex beings. The increasing complexity of the tasks robots are dedicated to is matched by an increasing complexity and versatility of the architectures now supporting conditioning or even elementary planning.

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.

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)

After critical appraisal of mathematical and biological characteristics of the model, we discuss how a classical hippocampal neural network expresses functions similar to those of the chaotic model, and then present an alternative stimulus-driven chaotic random recurrent neural network (RRNN) that learns patterns as well as sequences, and controls the navigation of a mobile robot.