二维二次非线性系统：双变量向量场(英文版)Two-Dimensional Qua

本书的重点是基于向量 场和二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和 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。本书详细探讨了 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，适用于 数学、机械和电气工程领域 的研究人员、学生和工程师 。

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-Bivariate Linear Systems 1.1 Single-Linear-Bivariate Linear Systems 1.2 One-Dimensional Flows and Switching Bifurcations 1.3 Two Linear-Bivariate Linear Systems References 2 Single-Linear-Bivariate Quadratic Systems 2.1 Constant and Linear-Bivariate Quadratic Vector Fields 2.2 Single-Bivariate Linear and Quadratic Vector Fields 2.2.1 Single-Bivariate Linear and Quadratic Systems 2.2.2 Flow Switching and Appearing Bifurcations 2.3 Two Quadratic Vector Fields with a Single-Bivariate Function 2.3.1 A Single-Linear-Bivariate Quadratic System 2.3.2 Appearing and Switching Bifurcations Reference 3 Linear-Bivariate Quadratic Dynamics 3.1 Linear and Quadratic Linear-Bivariate Vector Fields 3.2 Saddle-Focus and Saddle-Node Bifurcations 3.3 Two Linear-Bivariate Quadratic Vector Fields 3.4 Saddle-Focus Bifurcations and Global Dynamics 3.4.1 Saddle-Focus Appearing and Switching Bifurcations 3.4.2 Focus-Saddle Network Reference 4 Linear-Bivariate Product Quadratic Systems 4.1 Two Linear-Bivariate Product Quadratic Vector Fields 4.2 Linear-Bivariate-Product Quadratic Systems 4.2.1 With a Constant Vector Field 4.2.2 With a Linear-Bivariate Linear Vector Field 4.2.3 Two Linear-Bivariate Product Quadratic Vector Fields 4.2.4 Switching Bifurcations 4.3 Product and Single Linear-Bivariate Quadratic Vector Fields 4.4 Product and Single Linear-Bivariate Quadratic Dynamics 4.4.1 Saddle-Focus Bifurcations 4.4.2 Simple Equilibriums and Switching Bifurcations Reference 5 Nonlinear-Bivariate Quadratic Systems 5.1 Linear-Bivariate and Nonlinear-Bivariate Vector Fields 5.2 Nonlinear-Bivariate Quadratic Systems 5.2.1 With a Constant Vector Field 5.2.2 With a Linear-Bivariate Linear Vector Field 5.2.3 With a Two-Linear-Bivariate-Product Vector Field 5.3 Nonlinear and Single-Linear-Bivariate-Quadratic Vector Fields 5.4 Nonlinear and Single-Linear-Bivariate-Quadratic Dynamics 5.4.1 Saddle-Focus Bifurcations 5.4.2 Simple Equilibriums and Switching Bifurcations 5.5 Two Nonlinear Bivariate Quadratic Vector Fields 5.6 Nonlinear Bivariate Ouadratic Dynamics Reference Index