A quintic Z2-equivariant Liénard system arising from the complex Ginzburg-Landau equation: (II)
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912017280925696 |
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| author | Chen, Hebai Chen, Xingwu Jia, Man Tang, Yilei |
| author_facet | Chen, Hebai Chen, Xingwu Jia, Man Tang, Yilei |
| contents | 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., $a_2>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A quintic Z2-equivariant Liénard system arising from the complex Ginzburg-Landau equation: (II) Chen, Hebai Chen, Xingwu Jia, Man Tang, Yilei Classical Analysis and ODEs 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., $a_2>0$. |
| title | A quintic Z2-equivariant Liénard system arising from the complex Ginzburg-Landau equation: (II) |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.04024 |