Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type

Doug Zhou, Yi Sun, Aaditya Rangan, David Cai

Research output: Contribution to journalArticle

Abstract

We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.

Original languageEnglish (US)
Pages (from-to)229-245
Number of pages17
JournalJournal of Computational Neuroscience
Volume28
Issue number2
DOIs
StatePublished - Apr 2010

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Keywords

  • Firing-reset
  • Integrate-and-fire
  • Lyapunov exponents
  • Non-smooth
  • Refractory-induced degeneracy

ASJC Scopus subject areas

  • Cellular and Molecular Neuroscience
  • Cognitive Neuroscience
  • Sensory Systems

Cite this

Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type. / Zhou, Doug; Sun, Yi; Rangan, Aaditya; Cai, David.

In: Journal of Computational Neuroscience, Vol. 28, No. 2, 04.2010, p. 229-245.

Research output: Contribution to journalArticle

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