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Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol II : A Crossing-variable Cubic Vector Field / by Albert C. J. Luo.
- Format:
- Book
- Author/Creator:
- Luo, Albert C. J.
- Series:
- Engineering Series
- Language:
- English
- Subjects (All):
- Dynamics.
- Nonlinear theories.
- Engineering mathematics.
- Engineering--Data processing.
- Engineering.
- Functions of complex variables.
- Plasma waves.
- Applied Dynamical Systems.
- Mathematical and Computational Engineering Applications.
- Several Complex Variables and Analytic Spaces.
- Dynamical Systems.
- Waves, instabilities and nonlinear plasma dynamics.
- Local Subjects:
- Applied Dynamical Systems.
- Mathematical and Computational Engineering Applications.
- Several Complex Variables and Analytic Spaces.
- Dynamical Systems.
- Waves, instabilities and nonlinear plasma dynamics.
- Physical Description:
- 1 online resource (246 pages)
- Edition:
- 1st ed. 2024.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
- Summary:
- This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. 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-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Presents saddle flows plus third-order parabola flows and inflection flows as appearing flow bifurcations; Explains infinite-equilibriums for the switching of the first-order sink and source flows. .
- Contents:
- Constant and Self-Cubic Vector fields
- Self-linear and Self-cubic vector fields
- Self-quadratic and self-cubic vector fields
- Two self-cubic vector fields.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 9783031571084
- OCLC:
- 1472980314
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