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Homoclinic Networks Without 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 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.

Suggested Citation

  • Albert C. J. Luo, 2025. "Homoclinic Networks Without Centers," Springer Books, in: Limit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems, chapter 0, pages 7-46, Springer.
    • Handle: RePEc:spr:sprchp:978-981-97-2617-2_2
    DOI: 10.1007/978-981-97-2617-2_2
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