Mechanisms for frequency control in neuronal competition models

Rodica Curtu, Asya Shpiro, Nava Rubin, John Rinzel

Research output: Contribution to journalArticlepeer-review


We investigate analytically a firing rate model for a two-population network based on mutual inhibition and slow negative feedback in the form of spike frequency adaptation. Both neuronal populations receive external constant input whose strength determines the system's dynamical state-a steady state of identical activity levels or periodic oscillations or a winner-take-all state of bistability. We prove that oscillations appear in the system through supercritical Hopf bifurcations and that they are antiphase. The period of oscillations depends on the input strength in a nonmonotonic fashion, and we show that the increasing branch of the period versus input curve corresponds to a release mechanism and the decreasing branch to an escape mechanism. In the limiting case of infinitely slow feedback we characterize the conditions for release, escape, and occurrence of the winner-take-all behavior. Some extensions of the model are also discussed.

Original languageEnglish (US)
Pages (from-to)609-649
Number of pages41
JournalSIAM Journal on Applied Dynamical Systems
Issue number2
StatePublished - 2008


  • Antiphase oscillations
  • Binocular rivalry
  • Central pattern generators
  • Hopf bifurcation
  • Release and escape
  • Slow negative feedback
  • Winner-take-all

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation


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