Homoclinic Networks with Centers

Albert C. J. Luo ()
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Albert C. J. Luo: Southern Illinois University Edwardsville, Department of Mechanical and Mechatronics Engineering

Chapter Chapter 4 in Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems, 2025, pp 147-202 from Springer

Abstract: Abstract In this chapter, the homoclinic networks of positive and negative saddles with clockwise and counter-clockwise limit cycles in crossing-univariate polynomial systems are studied secondly, and the numbers of saddles and centers are determined through a theorem and the first integral manifolds are determined through polynomial functions. The corresponding proof of the theorem is given, and a few illustrations of networks of saddles and centers are given to show the corresponding geometric structures. Such homoclinic networks of saddles and centers are without any sources and sinks.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-97-2617-2_4

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DOI: 10.1007/978-981-97-2617-2_4

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