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Desynchronization in diluted neural networks

R. Zillmer·R. Livi·A. Politi·A. Torcini
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Abstract

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of ``stable chaos'', i.e. by observing that the stochastic-like behaviour is "limited" to a an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.

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R. Zillmer, R. Livi, A. Politi, A. Torcini. 2006-06-15. Desynchronization in diluted neural networks. https://doi.org/10.1103/physreve.74.036203

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