Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I
A Self-univariate Cubic Vector Field
Springer International Publishing
ISBN 978-3-031-48472-8
Standardpreis
Bibliografische Daten
eBook. PDF. Weiches DRM (Wasserzeichen)
2024
IX, 437 p. 32 illus., 31 illus. in color..
In englischer Sprache
Umfang: 437 S.
Verlag: Springer International Publishing
ISBN: 978-3-031-48472-8
Produktbeschreibung
This book, 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.
- Develops the theory for 1-dimensonal flow singularity and bifurcations to elucidate dynamics of nonlinear systems;
- Provides a new research direction in nonlinear dynamics community;
- Shows how singularity and bifurcations occur not only for equilibriums and attractors but also for 1-dimensional flows.
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