Transition frequencies in the neuronal oscillator

Yasuomi Sato

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


I present dynamical mechanisms responsible for transition frequencies, which are hidden in the homoclinic (HC) to supercritical Andronov-Hopf (AH) bifurcation switching in the two-dimensional Hindmarsh-Rose (2DHR) oscillator. For this purpose, I derive frequency gradients with respect to the input current and timescale in the 2DHR oscillator. The frequency gradients are formulated with phase response curves (PRCs) by expanding the firing frequency with small perturbations of the input current and timescale on the one-dimensional phase space of the 2DHR oscillator. I thus find two different types of striking breaks in the frequency plot with respect to the timescale, the sigmoid functional frequency and the discontinuous frequency. I also show effects of the unique PRC change on these transition frequencies.

Original languageEnglish
Article number58004
Issue number5
Publication statusPublished - 2013 Jun 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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