二维二次非线性系统：单变量向量场(英文版)Two-Dimensional Quadratic Nonlinear Syst

本书的重点是基于向量 场和一元二次函数的非线性 动力学。本书从不同视角研 究非线性动力学和二次动力 系统的分岔。二维动力系统 是非线性动力学中最简单的 动力系统之一，但二维二次 系统中平衡点和流的局部与 全局结构有助于我们理解其 他非线性动力系统，这也是 解决希尔伯特第十六问题的 关键一步。本书详细探论了 二维二次系统可能存在的奇 异动力学问题；介绍了二维 系统中平衡态和一维流的动 力学；讨论了鞍形汇和鞍形 源分岔，给出了鞍形中心分 岔；提出了无限平衡态是非 线性系统的开关分岔；从第 一类积分流形出发，发展了 鞍焦点网络，并给出了鞍、 源和汇网络。 本书可作为动力系统和 控制专业的参考书，适合数 学、机械和电气工程领域的 研究人员、学生和工程师阅 读参考。

罗朝俊教授为美国南伊利诺伊州州立大学终身教授、国际非线性系统领域知名学者。

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