平面分段线性系统中仅鞍被两条平行直线隔开的四交点极限环的存在性

Xiao-Juan Liu, Xiao-Song Yang
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引用次数: 0

摘要

本文研究了一类鞍由两条平行线分开的平面分段线性系统,主要研究了四交点极限环的存在性。给出了一个特殊的四交点极限环和一个异斜环的存在性的完整结论。在此基础上,给出了一般四交点极限环存在的充分条件。给出了一些例子来说明主要结果。
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Existence of Four-Intersection-Point Limit Cycles with Only Saddles Separated by Two Parallel Straight Lines in Planar Piecewise Linear Systems
In this paper, we study a family of planar piecewise linear systems with saddles separated by two parallel lines, and mainly investigate the existence of four-intersection-point limit cycles. We provide complete conclusions on the existence of a special four-intersection-point limit cycle and a heteroclinic loop. And, based on these results, we give some sufficient conditions for the existence of general four-intersection-point limit cycles. Some examples are given to illustrate the main results.
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