Changes in Repetitive Firing Rate Related to Phase Response Curves for Andronov–Hopf Bifurcations

doi:10.1088/0256-307X/31/5/050501

Chin. Phys. Lett.

2014, Vol. 31

Issue (05): 050501 DOI: 10.1088/0256-307X/31/5/050501

GENERAL

Changes in Repetitive Firing Rate Related to Phase Response Curves for Andronov–Hopf Bifurcations

Yasuomi D. Sato^1,2,3**

¹Department of Brain Science and Engineering, Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, 2-4, Hibikino, Wakamatsu, Kitakyushu, 808-0196, Japan
²Frankfurt Institute for Advanced Studies (FIAS), Johann Wolfgang Goethe University, Ruth-Moufang-Str.1, D60438, Frankfurt am Main, Germany
³Institute of Industrial Science, the University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo, 153-8505, Japan

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Yasuomi D. Sato 2014 Chin. Phys. Lett. 31 050501

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Abstract We study specific changes in repetitive firing in the two-dimensional Hindmarsh–Rose (2dHR) oscillatory system that undergoes a bifurcation transition from the supercritical Andronov–Hopf (AH) type to the subcritical Andronov–Hopf (SAH) type. We identify dynamical mechanisms which are responsible for changes of the repetitive firing rate during the AH to SAH bifurcation transitions. These include frequency-shift functions in response to small perturbations of a timescale parameter, its multiplicative parameter, and an external input current in the 2dHR oscillatory system. The frequency-shift functions are explicitly represented as functions relating to the phase response curves (PRCs). Then, we demonstrate that when the timescale is normal and relatively fast, the repetitive firing rate slightly increases and decreases respectively during the AH to SAH bifurcation transition with a change of the intrinsic parameter, whereas it decreases during the SAH to AH bifurcation transition with an increase in the timescale. By analyzing the three different frequency-shift functions, we show that such changes of the repetitive firing rate depend largely on changes of the PRC size. The PRC size for the SAH bifurcation shrinks to the PRC size for the AH bifurcation.

Published: 24 April 2014

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	87.19.ll	(Models of single neurons and networks)
	87.19.ln	(Oscillations and resonance)

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	Yasuomi D. Sato

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