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Two-dimensional Self and Product Cubic Systems, Vol. II

Crossing-linear and Self-quadratic Product Vector Field

Albert C. J. Luo

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Springer Nature Switzerland img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Allgemeines, Lexika

Beschreibung

This book is the thirteenth of 15 related monographs on Cubic Dynamical Systems, discusses self- and product-cubic systems with a crossing-linear and self-quadratic products vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed through up-down saddles, third-order concave-source (sink), and up-down-to-down-up saddles infinite-equilibriums. The author discusses how equilibrium networks with paralleled hyperbolic and hyperbolic-secant flows exist in such cubic systems, and the corresponding switching bifurcations obtained through the inflection-source and sink infinite-equilibriums. In such cubic systems, the appearing bifurcations are:

saddle-source (sink)

hyperbolic-to-hyperbolic-secant flows

double-saddle

third-order saddle, sink and source

third-order saddle-source (sink)

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Schlagwörter

Saddle-source (sink) appearing bifurcations, third-order concave-source (sink) infinite-equilibriums, Third-order saddle, source and sink appearing bifurcations, Third-order saddle (sink or source) appearing bifurcations, Crossing-linear and self-quadratic product vector field, Self-cubic vector field, inflection-source (sink) infinite-equilibrium, Hybrid networks of singular equilibriums and flows, Self and product cubic systems, Hyperbolic-to-hyperbolic-secant flow appearing bifurcations, up-down saddles infinite-equilibriums, Hybrid networks of saddles, centers, and hyperbolic flows, up-down-to-down-up saddle infinite-equilibriums, Double-saddle appearing bifurcations, Third-order saddle-source (sink) appearing bifurcations