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- ISBN:9787040602111
- 装帧:平装-胶订
- 册数:暂无
- 重量:暂无
- 开本:16开
- 页数:464
- 出版时间:2023-09-01
- 条形码:9787040602111 ; 978-7-04-060211-1
内容简介
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:详细讨论了二维二次系统可能的奇异动力学;给出了二元流形上平衡态和一维流的动力学;讨论了鞍焦点分岔,提出了基于无穷平衡点的开关分岔;证明了二元流形上的鞍焦点网络。
本书可作为动力系统和控制专业人员的参考书,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。
目录
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
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