AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART <TEX>$\chi$</TEX>'v= y, y' = 0

Han, Gil-Jun; Han, Gil-Jun

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P-ISSN3059-0604
E-ISSN3059-1309
KCI

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ISSN : 3059-0604

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Vol.4 No.1

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AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART $\chi$'v= y, y' = 0

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

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, 4(1), 61-69.

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Abstract

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

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

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논문 상세

Vol.4 No.1

AN UNFOLDING OF DEGENERATE EQUILIBRIA WITH LINEAR PART $\chi$'v= y, y' = 0

Abstract

한국수학교육학회지시리즈B:순수및응용수학