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Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I : A Self-univariate Cubic Vector Field / by Albert C. J. Luo.
- Format:
- Book
- Author/Creator:
- Luo, Albert C. J.
- Series:
- Engineering Series
- Language:
- English
- Subjects (All):
- Engineering mathematics.
- Mechanics, Applied.
- Dynamics.
- Nonlinear theories.
- System theory.
- Engineering Mathematics.
- Engineering Mechanics.
- Applied Dynamical Systems.
- Complex Systems.
- Local Subjects:
- Engineering Mathematics.
- Engineering Mechanics.
- Applied Dynamical Systems.
- Complex Systems.
- Physical Description:
- 1 online resource (442 pages)
- Edition:
- 1st ed. 2024.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
- 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.
- Contents:
- 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.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-031-48472-X
- OCLC:
- 1465361906
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