Changes of firing rate induced by changes of phase response curve in bifurcation transitions

Yasuomi D. Sato, Kazuyuki Aihara

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study dynamical mechanisms responsible for changes of the firing rate during four different bifurcation transitions in the two-dimensional Hindmarsh-Rose (2DHR) neuronmodel: the saddle node on an invariant circle (SNIC) bifurcation to the supercritical Andronov-Hopf (AH) one, the SNIC bifurcation to the saddle-separatrix loop (SSL) one, the AH bifurcation to the subcritical AH (SAH) one, and the SSL bifurcation to theAHone. For this purpose,we study slopes of the firing rate curvewith respect to not only an external input current but also temperature that can be interpreted as a timescale in the 2DHRneuron model. These slopes are mathematically formulated with phase response curves (PRCs), expanding the firing rate with perturbations of the temperature and external input current on the one-dimensional space of the phase S1 in the 2DHR oscillator. By analyzing the two different slopes of the firing rate curve with respect to the temperature and external input current, we find that during changes of the firing rate in all of the bifurcation transitions, the calculated slope with respect to the temperature also changes. This is largely dependent on changes in the PRC size that is also related to the slope with respect to the external input current. Furthermore, we find phase transition-like switches of the firing rate with a possible increase of the temperature during the SSL-to-AH bifurcation transition.

Original languageEnglish
Pages (from-to)2395-2418
Number of pages24
JournalNeural Computation
Volume26
Issue number11
DOIs
Publication statusPublished - 2014 Nov 20

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience

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