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Homoclinic Networks with Centers

In: Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems

Author

Listed:
  • Albert C. J. Luo

    (Southern Illinois University Edwardsville, Department of Mechanical and Mechatronics Engineering)

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.

Suggested Citation

  • Albert C. J. Luo, 2025. "Homoclinic Networks with Centers," Springer Books, in: Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems, chapter 0, pages 147-202, Springer.
    • Handle: RePEc:spr:sprchp:978-981-97-2617-2_4
    DOI: 10.1007/978-981-97-2617-2_4
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