二维二次非线性系统 单变量向量场

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。

   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

2.2Linear 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 Vector Fields

2.4 Singular Dynamics and Bifurcations

Reference

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