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230505 ||| eng |
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|a 9789811678738
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| 100 |
1 |
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|a Luo, Albert C. J.
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| 245 |
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|a Two-Dimensional Quadratic Nonlinear Systems
|h Elektronische Ressource
|b Volume I: Univariate Vector Fields
|c by Albert C. J. Luo
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| 250 |
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|a 1st ed. 2023
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| 260 |
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|a Singapore
|b Springer Nature Singapore
|c 2023, 2023
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| 300 |
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|a XIII, 685 p. 121 illus., 84 illus. in color
|b online resource
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| 505 |
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|a Chapter 1 Two-dimensional Linear Dynamical Systems -- Chapter 2 Single-variable Quadratic Systems with a Self-univariate Quadratic Vector Field -- Chapter 3 Single-variable Quadratic Systems with a Non-self-univariate Quadratic Vector Field -- Chapter 4 Variable-independent quadratic systems -- Chapter 5 Variable-crossing univariate quadratic systems -- Chapter 6 Two-univariate product quadratic systems -- Chapter 7 Product-bivariate Quadratic Systems with Self-univariate Vector Fields -- Chapter 8 Product-bivariate Quadratic Systems with Non-self-univariate Vector Fields
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| 653 |
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|a Applied Dynamical Systems
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| 653 |
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|a Differential Equations
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| 653 |
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|a Dynamical Systems
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| 653 |
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|a Complex Systems
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| 653 |
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|a Control and Systems Theory
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| 653 |
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|a Nonlinear theories
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| 653 |
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|a Dynamical systems
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| 653 |
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|a System theory
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| 653 |
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|a Dynamics
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| 653 |
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|a Control engineering
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| 653 |
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|a Differential equations
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Nonlinear Physical Science
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| 028 |
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|a 10.1007/978-981-16-7873-8
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| 856 |
4 |
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|u https://doi.org/10.1007/978-981-16-7873-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.39
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| 520 |
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|a 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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