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

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

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Apr 2010


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

ASJC Scopus subject areas

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience


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