A view of Neural Networks as dynamical systems

Abstract

We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective dynamics; 2. Statistical analysis of spikes trains; 3. Interplay between dynamics and network structure; 4. Effects of synaptic plasticity.

Review paper, 51 pages, 10 figures. submitted

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• Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality
• Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics
• Consistent model selection for estimating functional interactions among stochastic neurons with variable-length memory