Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I
Autor: | Albert C. J. Luo |
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EAN: | 9783031484728 |
eBook Format: | |
Sprache: | Englisch |
Produktart: | eBook |
Veröffentlichungsdatum: | 30.10.2024 |
Untertitel: | A Self-univariate Cubic Vector Field |
Kategorie: | |
Schlagworte: | Constant and self-cubic systems;Infinite-equilibriums;Crossing-linear and self-cubic systems;Two single-variable cubic systems;Appearing bifurcations;Inflection sinks sources and saddles;Up-down and down-up saddles;Crossing-quadratic and self-cubic |
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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.