Collective oscillations in disordered neural networks

Simona Olmi, Roberto Livi, Antonio Politi, Alessandro Torcini

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

We investigate the onset of collective oscillations in a excitatory pulse-coupled network of leaky integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O. V. Popovych , Phys. Rev. E 71 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N ->infinity, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogeneous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N-2, analogously to the scaling found for the "splay state.".

Original languageEnglish
Article number046119
Number of pages7
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume81
Issue number4
DOIs
Publication statusPublished - Apr 2010

Keywords

  • pulse-coupled oscillators
  • partial synchronization
  • neurons

Cite this

Collective oscillations in disordered neural networks. / Olmi, Simona; Livi, Roberto; Politi, Antonio; Torcini, Alessandro.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 81, No. 4, 046119, 04.2010.

Research output: Contribution to journalArticle

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