Singular Equilibria and Flows, and Simple Networks

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

Chapter Chapter 3 in Two-dimensional Crossing and Product Polynomial Systems, 2026, pp 295-470 from Springer

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-96-5715-5_3

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DOI: 10.1007/978-981-96-5715-5_3

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