Lorenz attractors in unfoldings of homoclinic-flip bifurcations

A. Golmakani; A.J. Homburg

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Lorenz attractors in unfoldings of homoclinic-flip bifurcations

机译：Lorenz吸引子在同斜翻转分叉的展开中

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摘要

Lorenz-like attractors are known to appear in unfoldings from certain codimension two homoclinic bifurcations for differential equations in R~3 that possess a reflectional symmetry. This includes homoclinic loops under a resonance condition and the inclination-flip homoclinic loops. We show that Lorenz-like attractors also appear in the third possible codimension two homoclinic bifurcation (for homoclinic loops to equilibria with real different eigenvalues); the orbit-flip homoclinic bifurcation. We moreover provide a bifurcation analysis computing the bifurcation curves of bifurcations from periodic orbits and discussing the creation and destruction of the Lorenz-like attractors. Known results for the inclination flip are extended to include a bifurcation analysis.

机译：已知在具有一定反射对称性的R〜3中，微分方程的某些同维两个同斜分叉的展开中会出现Lorenz状吸引子。这包括共振条件下的单斜环和倾斜-翻转单斜环。我们表明，类似Lorenz的吸引子也出现在第三个可能的维数两个同斜分叉中（对于同斜向的环，具有真实不同的特征值）；轨道翻转同宿分叉。此外，我们提供了分叉分析，该分叉分析计算了来自周期性轨道的分叉的分叉曲线，并讨论了Lorenz状吸引子的产生和破坏。倾斜翻转的已知结果扩展到包括分叉分析。

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来源
《Dynamical Systems》 |2011年第1期|p.61-76|共16页
作者
A. Golmakani; A.J. Homburg;
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作者单位

Department of Mathematics, Khayyam Institute of Higher Education, Mashhad, Iran,The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy;

KdV Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类
关键词
lorenz attractor; homoclinic bifurcation; orbit flip;

机译：洛伦兹吸引子同宿分叉;轨道翻转;

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Lorenz attractors in unfoldings of homoclinic-flip bifurcations

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