Thursday, January 17, 2013

1301.3779 (Gilles Wainrib et al.)

Optimal system size for complex dynamics in random neural networks near

Gilles Wainrib, Luis Carlos García del Molino
In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the subcritical regime : the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.
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