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In this chapter, a series of centers and saddles with hyperbolic singular flows in the crossing and product cubic systems is presented, and the corresponding switching dynamics are discussed through infinite equilibriums. The hyperbolic singular flows are the appearing bifurcations of hyperbolic and hyperbolic-secant flows. The up-down hyperbolic upper-to-lower saddles on the infinite equilibriums are the switching bifurcations of parabola-saddles with saddles and centers. The same directional saddles and centers are obtained in such cubic systems.

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Saddles, Centers, and Switching with Hyperbolic Singular Flows

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  • 发表日期：

    2025年

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  • Albert C. J. Luo

摘要

In this chapter, a series of centers and saddles with hyperbolic singular flows in the crossing and product cubic systems is presented, and the corresponding switching dynamics are discussed through infinite equilibriums. The hyperbolic singular flows are the appearing bifurcations of hyperbolic and hyperbolic-secant flows. The up-down hyperbolic upper-to-lower saddles on the infinite equilibriums are the switching bifurcations of parabola-saddles with saddles and centers. The same directional saddles and centers are obtained in such cubic systems.