Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I
A Self-univariate Cubic Vector Field
Luo, Albert C. J.
creator
author.
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SpringerLink (Online service)
text
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2024
1st ed. 2024.
monographic
eng
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IX, 437 p. 32 illus., 31 illus. in color. online resource.
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.
Chapter 1 Constant and Self-cubic Vector fields -- Chapter 2 Crossing-linear and Self-cubic Vector Fields -- Chapter 3 Crossing-quadratic and Self-Cubic Vector Fields -- Chapter 4 Two Single-variable Cubic Vector Fields.
by Albert C. J. Luo.
Engineering mathematics
Mechanics, Applied
Dynamics
Nonlinear theories
System theory
Engineering Mathematics
Engineering Mechanics
Applied Dynamical Systems
Complex Systems
TA329-348
Springer Nature eBook
9783031484728
https://doi.org/10.1007/978-3-031-48472-8
https://doi.org/10.1007/978-3-031-48472-8
241031
20251030113252.0
978-3-031-48472-8