Collective dynamics in the presence of finite-width pulses

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Abstract

The idealisation of neuronal pulses as $\delta$-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire neurons with delay and type-I phase-response curves. By exploring the role of the pulse-widths for different coupling strengths we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e. the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for $\delta$-spikes is smoothed out for finite-width pulses.
Original languageEnglish
Article number043135
Pages (from-to)043135
Number of pages13
JournalChaos
Volume31
Issue number4
Early online date23 Apr 2021
DOIs
Publication statusPublished - Apr 2021

Keywords

  • q-bio.NC
  • math.DS
  • nlin.AO

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