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Singular Equilibria and Flows, and Simple Networks

In: Two-dimensional Crossing and Product Polynomial Systems

Author

Listed:
  • Albert C. J. Luo

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

Abstract

In this chapter, the singular 1-dimensional flows and equilibriums in 2-dimensional polynomial systems are illustrated to help one understand the global bifurcations for networks of the hyperbolic and hyperbolic-secant flows with saddles and centers. The singular saddles and centers, parabola-saddles and inflection-saddles are presented, and the singular hyperbolic-flows, hyperbolic-to-hyperbolic-secant flows, inflection-source and sink flows, inflection-saddle flows are also presented. The infinite-equilibriums in the crossing and product polynomial systems are the appearing and switching bifurcations for hybrid networks of simple and singular equilibriums and flows. Such hybrid networks of simple equilibriums and flows are illustrated.

Suggested Citation

  • Albert C. J. Luo, 2026. "Singular Equilibria and Flows, and Simple Networks," Springer Books, in: Two-dimensional Crossing and Product Polynomial Systems, chapter 0, pages 295-470, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-5715-5_3
    DOI: 10.1007/978-981-96-5715-5_3
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