Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I A Self-univariate Cubic Vector Field /
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 discus...
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| Institution som forfatter: | |
| Format: | Electronisk eBog |
| Sprog: | engelsk |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Udgivelse: | 1st ed. 2024. |
| Fag: | |
| Online adgang: | https://doi.org/10.1007/978-3-031-48472-8 |
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| Summary: | 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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| Fysisk beskrivelse: | 1 online resource (IX, 437 p. 32 illus.). 31 illus. in color. |
| ISBN: | 9783031484728 |
| DOI: | 10.1007/978-3-031-48472-8 |