Phase-locking and bistability in neuronal networks with synaptic depression

Zeynep Akcay, Xinxian Huang, Farzan Nadim, Amitabha Bose

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris–Lecar neuron models.

Original languageEnglish (US)
Pages (from-to)8-21
Number of pages14
JournalPhysica D: Nonlinear Phenomena
StatePublished - Feb 1 2018

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Bistability
  • Coupled oscillators
  • Phase response curve
  • Short-term synaptic depression
  • Two-dimensional Poincarè map


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