author：
Chen, Hebai
(Chen, Hebai.)
[1]
|
Chen, Xingwu
(Chen, Xingwu.)
[2]
|
Jia, Man
(Jia, Man.)
[3]
|
Tang, Yilei
(Tang, Yilei.)
[4]
Unfold
Abstract：
In this paper, we study a quintic Liénard system x. = y, y. = -(a0x + a1x3 + a2x5) - (b0 + b1x2)y with 2-equivariance, arising from the complex Ginzburg-Landau equation. Although this system is a versal unfolding of the germ x. = y, y. = -a2x5 + O(x6) - (b1x2 + O(x3))y near the origin, it cannot be changed equivalently into a near-Hamiltonian system for global variables and parameters so that its dynamics cannot be studied via counting the isolate zeros of Abelian integrals as usual. We present a complete study of this system with a2 Copyright © by SIAM.
Keyword：
Dynamical systems
Hamiltonians
Hopf bifurcation
Classification
921 Mathematics - 931 Classical Physics; Quantum Theory; Relativity
Type
This work was financially supported by the National Key R&D Program of China (2022YFA1005900). The first and third authors were supported by the National Natural Science Foundation of China (12171485, 12322109). The second author was supported by the National Natural Science Foundations of China (12271378). The fourth author was supported by the National Natural Science Foundations of China (11931016, 12271355, 12161131001) and the Science and Technology Innovation Action Plan of Science and Technology Commission of Shanghai Municipality (STCSM, 20JC1413200). The authors sincerely thank Prof. Zhaosheng Feng for his great help during the writing of this paper. The authors sincerely thank reviewers and editors for their insightful comments and wonderful suggestions, which improved this paper greatly.
Access Number
EI:20234715096835
