Preface
Contents
1 Two-Dimensional Linear Dynamical Systems
1.1 Constant Vector Fields
1.2 Linear Vector Fields with a Single Variable
1.3 Variable-Independent Linear Vector Fields
1.4 Variable-Crossing Linear Vector Fields
1.5 Two Linear-Bivariate Vector Fields
Reference
2 Single-Variable Quadratic Systems with a Self-Univariate Quadratic Vector Field
2.1 Constant and Self-Univariate Quadratic Vector Fields
2.1.1 Self-Univariate Quadratic Systems with a Constant Vector Field
2.1.2 Singular Flows and Bifurcations
2.2 Linear and Self-Univariate Quadratic Vector Fields
2.2.1 Linear and Self-Univariate Quadratic Systems
2.2.2 Flow Switching and Appearing Bifurcations
2.3 Single-Variable Quadratic Systems with a Self-Univariate Vector Field
2.3.1 Variable-Crossing and Self-Univariate Quadratic Vector Fields
2.4 Singular Dynamics and Bifurcations
Reference
3 Single-Variable Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
3.1 Constant and Non-Self-Univariate Quadratic Vector Fields
3.1.1 Non-Self-Univariate Quadratic Systems with a Constant Vector Field
3.1.2 Singular Flows and Bifurcations
3.2 Linear and Non-Self-Univariate Quadratic Vector Fields
3.2.1 Linear and Non-Self-Univariate Quadratic Systems
3.2.2 Flow Switching and Appearing Bifurcations
3.3 With a Non-Self-Univariate Quadratic Vector Field
3.3.1 Quadratic Systems with a Non-Self-Univariate Vector Field
3.3.2 Singular Dynamics and Bifurcations
Reference
4 Variable-Independent Quadratic Dynamics
4.1 Constant and Variable-Independent Quadratic Vector Fields
4.2 Variable-Independent, Linear and Quadratic Vector Fields
4.2.1 Variable-Independent, Linear and Quadratic Systems
4.2.2 Saddle-Node Bifurcations and Global Dynamics
4.2.2.1 Saddle-Sink and Saddle-Source Bifurcations
4.2.2.2 Saddle-with-Sink and Saddle-with-Source
4.2.2.3 Appearing and Switching Bifurcations
4.3 Two Variable-Independent Univariate Quadratic Vector Fields
4.3.1 Two Variable-Independent Quadratic Global Dynamics
4.3.2 Singularity and Bifurcations
Reference
5 Variable-Crossing Univariate Quadratic Systems
5.1 Constant and Variable-Crossing Univariate Vector Fields
5.2 Linear and Quadratic Variable-Crossing Vector Fields
5.2.1 Linear and Quadratic Variable-Crossing Systems
5.2.2 Bifurcations and Limit Cycles
5.2.2.1 Singular Equilibriums
5.2.2.2 Limit Cycles and Separatrix with Center and Saddle
5.2.2.3 Appearing and Switching Bifurcations
5.3 Two Variable-Crossing Univariate Quadratic Vector Fields
5.3.1 Two Variable-Crossing Univariate Quadratic Systems
5.3.2 Bifurcations and Global Dynamics
5.3.2.1 Singular Equilibriums and Flows
5.3.2.2 Limit Cycles and Homoclinic Network
5.3.2.3 Appearing Bifurcations
Reference
6 Two-Univariate Product Quadratic Systems
6.1 Two-Univariate Product Quadratic Dynamics
6.2 Dynamics for Two-Univariate-Product Quadratic Systems
6.2.1 With a Constant Vector Field
6.2.2 With an Independent-Variable Linear Vector Field
6.2.3 With a Variable-Crossing Linear Vector Field
6.2.4 Two-Univariate Product Quadratic Vector Fields
6.2.5 Switching Bifurcations
Reference
7 Product-Bivariate Quadratic Systems with a Self-Univariate Quadratic Vector Field
7.1 Product-Bivariate and Self-Univariate Quadratic Dynamics
7.2 Singularity, Bifurcations and Global Dynamics
7.2.1 Saddle-Sink and Saddle-Source Bifurcations
7.2.2 Up-Down and Down-Up Upper-Saddles and Lower-Saddles
7.2.3 Simple Equilibriums with Hyperbolic Flows
7.2.4 Infinite-Equilibriums and Switching Bifurcations
Reference
8 Product-Bivariate Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
8.1 Product-Bivariate and Non-Self-Univariate Dynamics
8.2 Singularity, Bifurcations and Global Dynamics
8.2.1 Saddle-Center Appearing Bifurcations
8.2.2 Saddle-Saddle and Center-Center Bifurcations
8.2.3 Saddle and Center Flows with Hyperbolic Flows
8.2.4 Switching Bifurcations
Reference
Index

lgli/Two-Dimensional Quadratic Nonlinear Systems. Vol 1...Vector Fields 2023.pdf

lgrsnf/Two-Dimensional Quadratic Nonlinear Systems. Vol 1...Vector Fields 2023.pdf

zlib/Physics/Mechanics: Nonlinear dynamics and chaos/Albert C. J. Luo/Two-Dimensional Quadratic Nonlinear Systems: Volume 1 Univariate Vector Fields_24793733.pdf

Two-Dimensional Quadratic Nonlinear Systems : Volume I: Univariate Vector Fields

Luo, Albert C. J.

1st ed. 2023, Singapore, Singapore

S.l, 2022

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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.

Nonlinear Physical Science
Erscheinungsdatum: 21.04.2023

2023-04-24