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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Bibliographic Details
Main Author: Luo, Albert C. J.
Format: eBook
Language:English
Published: Singapore Springer Nature Singapore 2023, 2023
Edition:1st ed. 2023
Series:Nonlinear Physical Science
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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245 0 0 |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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260 |a Singapore  |b Springer Nature Singapore  |c 2023, 2023 
300 |a XIII, 685 p. 121 illus., 84 illus. in color  |b online resource 
505 0 |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 
653 |a Applied Dynamical Systems 
653 |a Differential Equations 
653 |a Dynamical Systems 
653 |a Complex Systems 
653 |a Control and Systems Theory 
653 |a Nonlinear theories 
653 |a Dynamical systems 
653 |a System theory 
653 |a Dynamics 
653 |a Control engineering 
653 |a Differential equations 
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520 |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