Symmetry breaking Hopf bifurcations in equations with O(2) symmetry with application to the kuramoto-sivashinsky equation

F.Amdjadi; P.J.Aston; P.Plechac

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Symmetry breaking Hopf bifurcations in equations with O(2) symmetry with application to the kuramoto-sivashinsky equation

机译：具有O（2）对称性的方程组中打破Hopf分支的对称性在kuramoto-sivashinsky方程中的应用

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In problems with O(2) symmetry, the Jacobian matrix at nontrivial steady state solutions with D_n symmetry always has a zero eigen- value due to the group orbit of solutions. We consider bifurcations which occur when complex eigenvalues also cross the imaginary axis and develop a numerical method which involves the addition of a new variable, namely the velocity of solutions drifting round the group orbit, and another equation, which has the form of a phase condition for isolating one solution on the group orbit.

机译：在具有O（2）对称性的问题中，由于解的群轨道，具有D_n对称性的非平稳态解的Jacobian矩阵始终具有零本征值。我们考虑了在复杂特征值也越过虚轴时发生的分叉，并开发了一种数值方法，其中涉及添加一个新变量，即溶液在群轨道上漂移的速度，以及另一个具有相态形式的方程。用于隔离群轨道上的一种解决方案。

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《Journal of Computational Physics》 |1997年第1期|p.181-192|共12页
作者
F.Amdjadi; P.J.Aston; P.Plechac;
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1. Symmetry-breaking bifurcation in O(2) x O(2)-symmetric nonlinear large problems and its application to the Kuramoto-Sivashinsky equation in two spatial dimensions [J] . Li CP, Yang ZH Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2004,第2期

机译：O（2）x O（2）对称非线性大问题中的对称破缺分支及其在二维空间中的Kuramoto-Sivashinsky方程中的应用
2. Hopf bifurcations of functional differential equations with dihedral symmetries [J] . Krawcewicz W., Wu J., Vivi P. Journal of Differential Equations . 1998,第1期

机译：具有二面对称性的泛函微分方程的Hopf分支
3. Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations [J] . Peng MS Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2005,第5期

机译：一类时滞微分方程的欧拉方法中的对称破坏，分支，周期和混沌
4. Lie Symmetry Analysis and Exact Solutions for the Coupled Kuramoto-Sivashinsky Equations [C] . Yan Fang, Hua Cuncai, Liu Haihong, 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications . 2011

机译：耦合的Kuramoto-Sivashinsky方程的Lie对称性分析和精确解
5. Bifurcation analysis of a class of delay-differential equations with reflectional symmetry: Applications to ENSO. [D] . Redmond, Brian F. 2002

机译：一类具有反射对称性的时滞微分方程的分叉分析：在ENSO中的应用。
6. Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations [O] . Rachadawan Darlai, Elvin J. Moore, Sanoe Koonprasert -1

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7. Hopf Bifurcations of Functional Differential Equations with Dihedral Symmetries [O] . Krawcewicz W, Vivi P, Wu J 1998

机译：具有二面对称的泛函微分方程的Hopf分支。
8. Schwinger Dyson equations: Dynamical chiral symmetry breaking and confinement [R] . Roberts, C D 1992

机译：schwinger Dyson方程：动态手征对称破缺和约束

Symmetry breaking Hopf bifurcations in equations with O(2) symmetry with application to the kuramoto-sivashinsky equation

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