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Bifurcation of a Modified BVP Circuit Model for Neurons Generating Rectangular Waves

Kunichika TSUMOTO, Tetsuya YOSHINAGA, Hiroshi KAWAKAMI

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Summary :

We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhöffer-van der Pol equation, which is considered as a circuit model for neurons of a feeding rhythm generator. In particular, we clarify a mechanism of properties in a one-parameter graph on the period of oscillations, showing a staircase with hysteresis jumps, by studying a successive bifurcation process including a chain of homoclinic bifurcations. The occurrence of homoclinic bifurcations is confirmed by using the linking number of limit cycles related with the stable manifold through an equilibrium.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1729-1736
Publication Date
1999/09/25
Publicized
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Type of Manuscript
Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
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