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

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031918. doi: 10.1103/PhysRevE.80.031918. Epub 2009 Sep 28.

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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Electric Conductivity
  • Models, Neurological
  • Nerve Net / cytology*
  • Nerve Net / physiology
  • Neurons / cytology*
  • Nonlinear Dynamics*
  • Stochastic Processes
  • Time Factors