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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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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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AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART <TEX>$\chi$</TEX>'v= y, y' = 0

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Dankook University)
Han, Gil-Jun. (1997). AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART <TEX>$\chi$</TEX>'v= y, y' = 0. 한국수학교육학회지시리즈B:순수및응용수학, 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

한국수학교육학회지시리즈B:순수및응용수학

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