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Two-dimensional Product-Cubic Systems, Vol. I

Constant and Linear Vector Fields

Albert C. J. Luo

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Springer Nature Switzerland img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Sonstiges

Beschreibung

This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center.  

Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations. 


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Schlagwörter

Parabola-saddle bifurcations, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Saddle-source (sink) bifurcations, Inflection-source (sink) Infinite-equilibriums I, Infinite-equilibrium switching bifurcations, Inflection-sinks and sources, Constant and product-cubic systems, Connected hyperbolic and hyperbolic-secant flows