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Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I

A Self-univariate Cubic 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 first of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of self-variables and are discussed as the first part of the book. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-dimensional cubic systems are for the first time to be presented. Third-order source and sink flows are presented, and the third-order parabola flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order source and sink flows, and the second-order saddle flows with the first and third-order parabola flows, and the inflection flows. The appearing bifurcations in such cubic systems includes saddle flows and third-order source (sink) flows, inflection flows and third-order up (down)-parabola flows.

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Schlagwörter

Infinite-equilibriums, Up-down and down-up saddles, Constant and self-cubic systems, Crossing-quadratic and self-cubic systems, Switching bifurcations, Third-order sink and source flows and saddle flows, Logarithmic and concave sinks and sources, Two single-variable cubic systems, Parabola sinks, sources and saddles, Third-order parabola flows and inflection flows, Crossing-linear and self-cubic systems, Inflection sinks, sources and saddles, Appearing bifurcations