二维二次非线性系统

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 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-Uni-variate Vector Field 2.3.1 Variable-Crossing and Self-Univariate Quadratic 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