二维二次非线性系统：单变量向量场（英文版）
定价：￥199.00
作者： 罗朝俊
出版社：高等教育出版社
- 高等教育出版社
- 9787040604955
- 1版
- 64277283-4
- 16开
- 980
- 理学
- 物理学类
- 物理类
- 研究生及以上
目录
目录
前辅文
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
4.3 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
5.3 Two Variable-Crossing Univariate Quadratic Vector Fields
5.3.1 Two Variable-Crossing Univariate Quadratic Systems
5.3.2 Bifurcations and Global Dynamics
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
前辅文
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
4.3 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
5.3 Two Variable-Crossing Univariate Quadratic Vector Fields
5.3.1 Two Variable-Crossing Univariate Quadratic Systems
5.3.2 Bifurcations and Global Dynamics
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
前辅文
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
4.3 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
5.3 Two Variable-Crossing Univariate Quadratic Vector Fields
5.3.1 Two Variable-Crossing Univariate Quadratic Systems
5.3.2 Bifurcations and Global Dynamics
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
前辅文
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
4.3 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
5.3 Two Variable-Crossing Univariate Quadratic Vector Fields
5.3.1 Two Variable-Crossing Univariate Quadratic Systems
5.3.2 Bifurcations and Global Dynamics
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
