Two-Dimensional Quadratic Nonlinear Systems
Volume I: Univariate Vector Fields
(Sprache: Englisch)
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...
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Klappentext zu „Two-Dimensional Quadratic Nonlinear Systems “
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.
Inhaltsverzeichnis zu „Two-Dimensional Quadratic Nonlinear Systems “
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.
Autoren-Porträt von Albert C. J. Luo
Prof. Albert C. J. Luo is a Distinguished Research Professor at the Department of Mechanical Engineering at Southern Illinois University Edwardsville, USA. He received his Ph.D. degree from the University of Manitoba, Canada, in 1995. His research focuses on nonlinear dynamics, nonlinear mechanics and nonlinear differential equations , and he has published over 40 books and more than 350 journal articles and conference papers in these fields. He received the Paul Simon Outstanding Scholar Award in 2008 and an ASME fellowship in 2007. He was an editor for Communications in Nonlinear Science and Numerical Simulation, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics. He now serves as Co-editor of the Journal of Applied Nonlinear Dynamics and Editor of various book series, including "Nonlinear Systems and Complexity" and "Nonlinear Physical Science."His major contributions on nonlinear dynamical systems are:
Bibliographische Angaben
- Autor: Albert C. J. Luo
- 2023, 1st ed. 2023, XIII, 685 Seiten, 84 farbige Abbildungen, Masse: 15,5 x 23,5 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 9811678723
- ISBN-13: 9789811678721
Sprache:
Englisch
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