Mode Bifurcations in Diffusively Coupled Van der Pol Equations

Tetsuya YOSHINAGA; Hiroshi KAWAKAMI; Kenichi YOSHIKAWA

Mode Bifurcations in Diffusively Coupled Van der Pol Equations

Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, Kenichi YOSHIKAWA

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Bifurcations of phase-locked modes for diffusively coupled van der Pol equations are investigated. It is known that in-phase and out-of-phase modes are typically observed in the system if two oscillatory equations are identical. There have been many studies on the behavior of diffusively coupled equations of van der Pol type. Many of these, however, persist in the limits of weakly nonlinearity and weak coupling. In this paper we study global feature of bifurcation sets of the modes under relatively wide range of variation of system parameters: coefficient of nonlinear term, parameter related to the frequency of the uncoupled equations, diffusion coefficient and so on.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1420-1427

Publication Date: 1991/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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Tetsuya YOSHINAGA
Hiroshi KAWAKAMI
Kenichi YOSHIKAWA

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Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, Kenichi YOSHIKAWA, "Mode Bifurcations in Diffusively Coupled Van der Pol Equations" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 6, pp. 1420-1427, June 1991, doi: .
Abstract: Bifurcations of phase-locked modes for diffusively coupled van der Pol equations are investigated. It is known that in-phase and out-of-phase modes are typically observed in the system if two oscillatory equations are identical. There have been many studies on the behavior of diffusively coupled equations of van der Pol type. Many of these, however, persist in the limits of weakly nonlinearity and weak coupling. In this paper we study global feature of bifurcation sets of the modes under relatively wide range of variation of system parameters: coefficient of nonlinear term, parameter related to the frequency of the uncoupled equations, diffusion coefficient and so on.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1420/_p

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@ARTICLE{e74-a_6_1420,
author={Tetsuya YOSHINAGA, Hiroshi KAWAKAMI, Kenichi YOSHIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Mode Bifurcations in Diffusively Coupled Van der Pol Equations},
year={1991},
volume={E74-A},
number={6},
pages={1420-1427},
abstract={Bifurcations of phase-locked modes for diffusively coupled van der Pol equations are investigated. It is known that in-phase and out-of-phase modes are typically observed in the system if two oscillatory equations are identical. There have been many studies on the behavior of diffusively coupled equations of van der Pol type. Many of these, however, persist in the limits of weakly nonlinearity and weak coupling. In this paper we study global feature of bifurcation sets of the modes under relatively wide range of variation of system parameters: coefficient of nonlinear term, parameter related to the frequency of the uncoupled equations, diffusion coefficient and so on.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Mode Bifurcations in Diffusively Coupled Van der Pol Equations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1420
EP - 1427
AU - Tetsuya YOSHINAGA
AU - Hiroshi KAWAKAMI
AU - Kenichi YOSHIKAWA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - Bifurcations of phase-locked modes for diffusively coupled van der Pol equations are investigated. It is known that in-phase and out-of-phase modes are typically observed in the system if two oscillatory equations are identical. There have been many studies on the behavior of diffusively coupled equations of van der Pol type. Many of these, however, persist in the limits of weakly nonlinearity and weak coupling. In this paper we study global feature of bifurcation sets of the modes under relatively wide range of variation of system parameters: coefficient of nonlinear term, parameter related to the frequency of the uncoupled equations, diffusion coefficient and so on.
ER -