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。

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