Analysis of generation mechanism of very slow neuronal rhythm through a Hopf bifurcation

Yusuke Nii; Shinji Doi; Sadatoshi Kumagai

doi:10.11499/sicep.2002.0.371.0

SICE Annual Conference 2002

DOI https://doi.org/10.11499/sicep.2002.0.371.0

Conference information

Host: The Society of Instrument and Control Engineers

Co-host: IEEE/Industiral Electronic Society, IEEE/Robotics and Automation Society, IEEE/Control System Society

Analysis of generation mechanism of very slow neuronal rhythm through a Hopf bifurcation

Yusuke Nii, Shinji Doi, Sadatoshi Kumagai

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Keywords: Bonhoeffer-van der Pol equation, singular Hopf bifurcation, slow oscillation, homoclinic bifurcation

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Pages 371

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Abstract

Using Bonhoeffer-van der Pol (BVP) equation extended to three variables, it is shown that this single neuron model can produce an extraordinarily slow oscillation through a Hopf bifurcation. The generation mechanism of such neuronal rhythm is analyzed from a viewpoint of a bifurcation theory.

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