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Two-dimensional quadratic nonlinear ...

Luo, Albert C. J.

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Two-dimensional quadratic nonlinear systemss.. Volume I,. Univariate vector fields

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two-dimensional quadratic nonlinear systemss./ by Albert C. J. Luo.
remainder title:	Univariate vector fields
Author:	Luo, Albert C. J.
Published:	Singapore :Springer Nature Singapore : : 2023.,
Description:	xiii, 685 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Nonlinear systems. -
Online resource:	https://doi.org/10.1007/978-981-16-7873-8
ISBN:	9789811678738

Two-dimensional quadratic nonlinear systemss.. Volume I,. Univariate vector fields
Luo, Albert C. J.

Two-dimensional quadratic nonlinear systemss.Volume I,Univariate vector fields[electronic resource] /Univariate vector fieldsby Albert C. J. Luo. - Singapore :Springer Nature Singapore :2023. - xiii, 685 p. :ill., digital ;24 cm. - Nonlinear physical science,1867-8459. - 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.

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.

ISBN: 9789811678738

Standard No.: 10.1007/978-981-16-7873-8doiSubjects--Topical Terms:

686475
Nonlinear systems.

LC Class. No.: QA402 / .L86 2023

Dewey Class. No.: 03.75

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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.
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