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Title
Two-dimensional quadratic nonlinear systems. Volume I, Univariate vector fields / Albert C.J. Luo.
ISBN
9789811678738 electronic book
9811678731 electronic book
9789811678721
9811678723
Published
Singapore : Springer, 2023.
Language
English
Description
1 online resource (1 volume) : illustrations (black and white, and color).
Item Number
10.1007/978-981-16-7873-8 doi
Call Number
QA402 .L86 2023
Dewey Decimal Classification
003/.75
Summary
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 Hilberts 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Nonlinear physical science.
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.
