Degenerate hopf bifurcations in discontinuous planar systems
Degenerate hopf bifurcations in discontinuous planar systems
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DOI：
10.1006/jmaa.2000.7188
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发表时间：
2001-01
影响因子：
1.3
通讯作者：
B. Coll;A. Gasull;R. Prohens
中科院分区：
文献类型：
--
作者：
B. Coll;A. Gasull;R. Prohens
摘要研究了具有间断线的平面间断微分方程奇点的稳定性。对于最一般的情况，这是通过计算某种李雅普诺夫常数来完成的。我们的计算是基于所谓的（R，θ，p，q）-广义极坐标，由李雅普诺夫引进，它们是本质上不同于所使用的光滑情况。这些李雅普诺夫常数也被用来产生一些具体的例子的极限环。
Abstract We study the stability of a singular point for planar discontinuous differential equations with a line of discontinuities. This is done, for the most generic cases, by computing some kind of Lyapunov constants. Our computations are based on the so called ( R , θ, p , q )-generalized polar coordinates, introduced by Lyapunov, and they are essentially different from the ones used in the smooth case. These Lyapunov constants are also used to generate limit cycles for some concrete examples.