Desynchronization in diluted neural networks

TL;DR

This paper studies how weakly diluted inhibitory neural networks transition from regular to irregular activity as coupling strength increases, revealing a phenomenon akin to stable chaos with long-lasting transient dynamics.

Contribution

It demonstrates the existence of a long transient regime in diluted neural networks where irregular activity persists despite negative Lyapunov exponents, linking it to stable chaos.

Findings

Transition from regular to stochastic-like dynamics with increased coupling

Irregular activity is a long transient despite negative Lyapunov exponent

Transient dynamics are stationary and system-size dependent

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.