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Uniqueness of Limit Cycle for the Quadratic Systems with Weak Saddle and Focus

✍ Scribed by Shen Qi Zhao; Ping Guang Zhang


Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2004
Tongue
English
Weight
140 KB
Volume
20
Category
Article
ISSN
1439-7617

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πŸ“œ SIMILAR VOLUMES


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✍ C.Z. Li; J. Llibre; Z.F. Zhang πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 781 KB

We study the bounded quadratic systems with either two weak foci or a weak focus of order 2. From the first case we obtain (1,1)-configuration of limit cycles, and in the second case we prove that there is no limit cycle surrounding the weak focus of order 2. Also, we unfold the bounded quadratic sy

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We know five different families of algebraic limit cycles in quadratic systems, one of degree 2 and four of degree 4. Moreover, if there are other families of algebraic limit cycles for quadratic systems, then their degrees must be larger than 4. It is known that if a quadratic system has an algebra