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arXiv · 2409.04024

A quintic Z2-equivariant Liénard system arising from the complex Ginzburg-Landau equation: (II)

Hebai Chen·Xingwu Chen·Man Jia·Yilei Tang
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Abstract

We continue to study a quintic Z2-equivariant Liénard system $\dot x=y,\dot y=-(a_0x+a_1x^3+a_2x^5)-(b_0+b_1x^2)y$ with $a_2b_1\ne 0$, arising from the complex Ginzburg-Landau equation. Global dynamics of the system have been studied in [{\it SIAM J. Math. Anal.}, {\bf 55}(2023) 5993-6038] when the sum of the indices of all equilibria is $-1$, i.e., $a_2<0$. The aim of this paper is to study the global dynamics of this quintic Liénard system when the sum of the indices of all equilibria is $1$, i.e., $a_2>0$.

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Hebai Chen, Xingwu Chen, Man Jia, Yilei Tang. 2024-09-06. A quintic Z2-equivariant Liénard system arising from the complex Ginzburg-Landau equation: (II). https://arxiv.org/abs/2409.04024

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