论文标题
广义雷利 - 莱纳德振荡器中极限周期数的下限
Lower bounds for the number of limit cycles in a generalized Rayleigh-Liénard oscillator
论文作者
论文摘要
在本文中，考虑了一个广义的雷利 - 莱纳德振荡器，并提供了从弱焦点平衡和鞍座连接中分叉的极限周期数的下限。通过假设对所考虑系统的参数进行一些开放条件，可以提供超过十二个限制周期的存在。更准确地说，该方法包括在某些特定参数的符号中执行适当的更改，并应用Poincaré-Bendixson定理来确保存在极限周期。特别是，明确显示了通过转介方法获得极限周期的方法。本研究中应用的主要技术是Lyapunov常数和Melnikov方法。
In this paper a generalized Rayleigh-Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approach consists in perform suitable changes in the sign of some specific parameters and apply Poincaré-Bendixson Theorem for assure the existence of limit cycles. In particular, the method for obtaining the limit cycles through the referred approach is explicitly exhibited. The main techniques applied in this study are the Lyapunov constants and the Melnikov method.
