Two-dimensional Single-Variable Cubic Nonlinear Systems, Vol. I
Springer International Publishing (Verlag)
978-3-031-48471-1 (ISBN)
This book is 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.
Dr. Albert C. J. Luo is a Distinguished Research Professor at the Southern Illinois University Edwardsville, in Edwardsville, IL, USA. Dr. Luo worked on Nonlinear Mechanics, Nonlinear Dynamics, and Applied Mathematics. He proposed and systematically developed: (i) the discontinuous dynamical system theory, (ii) analytical solutions for periodic motions in nonlinear dynamical systems, (iii) the theory of dynamical system synchronization, (iv) the accurate theory of nonlinear deformable-body dynamics, (v) new theories for stability and bifurcations of nonlinear dynamical systems. He discovered new phenomena in nonlinear dynamical systems. His methods and theories can help understanding and solving the Hilbert sixteenth problems and other nonlinear physics problems. The main results were scattered in 45 monographs in Springer, Wiley, Elsevier, and World Scientific, over 200 prestigious journal papers, and over 150 peer-reviewed conference papers.
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.
| Erscheinungsdatum | 08.09.2024 |
|---|---|
| Zusatzinfo | IX, 437 p. 32 illus., 31 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Technik ► Maschinenbau | |
| Schlagworte | appearing bifurcations • Constant and self-cubic systems • Crossing-linear and self-cubic systems • Crossing-quadratic and self-cubic systems • Infinite-equilibriums • Inflection sinks, sources and saddles • Logarithmic and concave sinks and sources • Parabola sinks, sources and saddles • switching bifurcations • Third-order parabola flows and inflection flows • Third-order sink and source flows and saddle flows • Two single-variable cubic systems • Up-down and down-up saddles |
| ISBN-10 | 3-031-48471-1 / 3031484711 |
| ISBN-13 | 978-3-031-48471-1 / 9783031484711 |
| Zustand | Neuware |
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