Network-induced chaos in integrate-and-fire neuronal ensembles

Douglas Zhou, Aaditya V. Rangan, Yi Sun, David Cai

Research output: Contribution to journalArticlepeer-review

Abstract

It has been shown that a single standard linear integrate-and-fire (IF) neuron under a general time-dependent stimulus cannot possess chaotic dynamics despite the firing-reset discontinuity. Here we address the issue of whether conductance-based, pulsed-coupled network interactions can induce chaos in an IF neuronal ensemble. Using numerical methods, we demonstrate that all-to-all, homogeneously pulse-coupled IF neuronal networks can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a precise characterization of the largest Lyapunov exponent for these high dimensional nonsmooth dynamical systems. In addition, we present a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent, which can overcome difficulties encountered by traditional methods for these nonsmooth dynamical systems with degeneracy induced by, e.g., refractoriness of neurons.

Original languageEnglish (US)
Article number031918
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume80
Issue number3
DOIs
StatePublished - Sep 28 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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