Two-Dimensional Quadratic Nonlinear Systems Volume I: Univariate Vector Fields /
This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical syste...
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| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Lenguaje: | inglés |
| Publicado: |
Singapore :
Springer Nature Singapore : Imprint: Springer,
2023.
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| Edición: | 1st ed. 2023. |
| Colección: | Nonlinear Physical Science,
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| Materias: | |
| Acceso en línea: | https://doi.org/10.1007/978-981-16-7873-8 |
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| Sumario: | This book focuses on the nonlinear dynamics based on the vector fields with univariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems. It provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems. Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem. Possible singular dynamics of the two-dimensional quadratic systems are discussed in detail. The dynamics of equilibriums and one-dimensional flows in two-dimensional systems are presented. Saddle-sink and saddle-source bifurcations are discussed, and saddle-center bifurcations are presented. The infinite-equilibrium states are switching bifurcations for nonlinear systems. From the first integral manifolds, the saddle-center networks are developed, and the networks of saddles, source, and sink are also presented. This book serves as a reference book on dynamical systems and control for researchers, students, and engineering in mathematics, mechanical, and electrical engineering. |
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| Descripción Física: | XIII, 685 p. 121 illus., 84 illus. in color. online resource. |
| ISBN: | 9789811678738 |
| ISSN: | 1867-8459 |
| DOI: | 10.1007/978-981-16-7873-8 |