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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.4 No.1

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1997, v.4 no.1, pp.61-69
Han, Gil-Jun
Han,, G. (1997). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 4(1), 61-69.

Abstract

In this paper, we study the dynamics of a two-parameter unfolding system <TEX>$\chi$</TEX>' = y, y' = <TEX>$\beta$</TEX>y＋<TEX>$\alpha$</TEX>f(<TEX>$\chi\alpha\pm\chiy$</TEX>＋yg(<TEX>$\chi$</TEX>), where f(<TEX>$\chi$</TEX>,<TEX>$\alpha$</TEX>) is a second order polynomial in <TEX>$\chi$</TEX> and g(<TEX>$\chi$</TEX>) is strictly nonlinear in <TEX>$\chi$</TEX>. We show that the higher order term yg(<TEX>$\chi$</TEX>) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small <TEX>$\alpha$</TEX> and <TEX>$\beta$</TEX> if the nontrivial fixed point approaches to the origin as <TEX>$\alpha$</TEX> approaches zero.

keywords
Double zero eigenvalue, Nilpotent singularity, Normal form, Unfolding, Hopf bifurcation, Codimension

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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