Homoclinic Networks Without 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 2 in Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems, 2025, pp 7-46 from Springer

Abstract: Abstract In this Chapter, the homoclinic networks of sources, sinks, and saddles in self-univariate polynomial systems are discussed, and the numbers of sources, sinks and saddles are determined through a theorem, and the first integral manifolds are developed. The corresponding proof of the theorem is completed and a few illustrations of networks for source, sinks and saddles are presented for a better understanding of the homoclinic networks. Such homoclinic networks are without any centers even if the networks are separated by the homoclinic orbits.

Date: 2025
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DOI: 10.1007/978-981-97-2617-2_2

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