Two-dimensional quadratic nonlinear systems : univariate vector fields / Albert C. J. Luo.

Format:

Book

Author/Creator:

Luo, Albert C. J., author.

Series:

Nonlinear Physical Science, 1867-8459

Language:

English

Subjects (All):

Computational complexity.

Nonlinear systems.

Physical Description:

1 online resource (XIII, 685 p. 121 illus., 84 illus. in color.)

Edition:

1st ed. 2023.

Place of Publication:

Singapore : Springer, [2023]

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 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.

Contents:

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.

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

981-16-7873-1