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Article Dans Une Revue The Journal of Chemical Physics Année : 2013

Optimal system size for complex dynamics in random neural networks near criticality.

Résumé

: In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259-262 (1988)] in the context of random neural networks. When system size is infinite, 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 sub-critical regime for finite size systems: 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.

Dates et versions

hal-00946223 , version 1 (13-02-2014)

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Gilles Wainrib, Luis Carlos García del Molino. Optimal system size for complex dynamics in random neural networks near criticality.. The Journal of Chemical Physics, 2013, 23 (4), pp.043134. ⟨10.1063/1.4841396⟩. ⟨hal-00946223⟩
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