Bifurcation of Burst Oscillations with Rectangular Waveform Observed in a Modified BVP Equation as a Neuron Model

• TSUMOTO Kunichika

  Faculty of Engineering, The University of Tokushima

• YOSHINAGA Tetsuya

  Faculty of Engineering, The University of Tokushima

• KAWAKAMI Hiroshi

  Faculty of Engineering, The University of Tokushima

Bibliographic Information

Other Title

• ニューロンモデルとしての拡張BVP方程式にみられる矩形波バースト振動の分岐

Abstract

We investigate bifurcations of burst oscillations with rectangular waveform observed in a modified Bonhoeffer-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.

Journal

• IEICE technical report. Nonlinear problems

  IEICE technical report. Nonlinear problems 98 (582), 43-50, 1999-02-08

  The Institute of Electronics, Information and Communication Engineers

Keywords

• rectangular wave
• homoclinic orbit
• linking number
• bifurcation
• nonlinear circuit

Details

• CRID: 1570009752433006720
• NII Article ID: 110003292147
• NII Book ID: AN10060800
• Text Lang: ja
• Data Source:
  • CiNii Articles