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Two-Dimensional Quadratic Nonlinear Systems: Volume II: Bivariate Vector Fields (Nonlinear Physical Science) 🔍
Albert C. J. Luo Springer Nature Singapore Pte Ltd Fka Springer Science + Business Media Singapore Pte Ltd, Nonlinear Physical Science Ser, Singapore, 2022
英语 [en] · PDF · 5.9MB · 2022 · 📘 非小说类图书 · 🚀/lgli/upload/zlib · Save
描述
The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.
备用文件名
lgli/Albert C. J. Luo - Two-Dimensional Quadratic Nonlinear Systems: Volume II: Bivariate Vector Fields (2022, Springer).pdf
备用文件名
zlib/Mathematics/Geometry and Topology/Albert C. J. Luo/Two-Dimensional Quadratic Nonlinear Systems: Volume II: Bivariate Vector Fields_21768949.pdf
备选标题
Two-Dimensional Quadratic Nonlinear Systems: Volume I: Univariate Vector Fields
备选作者
Luo, Albert C. J.
备用版本
Nonlinear physical science, Singapore, 2021
备用版本
Springer Nature, Singapore, 2022
备用版本
Singapore, Singapore
备用版本
1st ed. 2021, 2022
备用版本
2, 20220329
元数据中的注释
producers:
iText® 5.5.13.2 ©2000-2020 iText Group NV (AGPL-version); modified using iText® 7.1.14 ©2000-2020 iText Group NV (AGPL-version)
备用描述
Preface 7
Contents 8
1 Two-Dimensional Linear-Bivariate Linear Systems 10
1.1 Single-Linear-Bivariate Linear Systems 10
1.2 One-Dimensional Flows and Switching Bifurcations 26
1.3 Two Linear-Bivariate Linear Systems 39
References 46
2 Single-Linear-Bivariate Quadratic Systems 47
2.1 Constant and Linear-Bivariate Quadratic Vector Fields 47
2.2 Single-Bivariate Linear and Quadratic Vector Fields 73
2.2.1 Single-Bivariate Linear and Quadratic Systems 73
2.2.2 Flow Switching and Appearing Bifurcations 97
2.3 Two Quadratic Vector Fields with a Single-Bivariate Function 122
2.3.1 A Single-Linear-Bivariate Quadratic System 122
2.3.2 Appearing and Switching Bifurcations 148
Reference 163
3 Linear-Bivariate Quadratic Dynamics 164
3.1 Linear and Quadratic Linear-Bivariate Vector Fields 164
3.2 Saddle-Focus and Saddle-Node Bifurcations 177
3.3 Two Linear-Bivariate Quadratic Vector Fields 189
3.4 Saddle-Focus Bifurcations and Global Dynamics 207
3.4.1 Saddle-Focus Appearing and Switching Bifurcations 207
3.4.2 Focus-Saddle Network 213
Reference 225
4 Linear-Bivariate Product Quadratic Systems 226
4.1 Two Linear-Bivariate Product Quadratic Vector Fields 226
4.2 Linear-Bivariate-Product Quadratic Systems 267
4.2.1 With a Constant Vector Field 267
4.2.2 With a Linear-Bivariate Linear Vector Field 270
4.2.3 Two Linear-Bivariate Product Quadratic Vector Fields 277
4.2.4 Switching Bifurcations 284
4.3 Product and Single Linear-Bivariate Quadratic Vector Fields 294
4.4 Product and Single Linear-Bivariate Quadratic Dynamics 313
4.4.1 Saddle-Focus Bifurcations 314
4.4.2 Simple Equilibriums and Switching Bifurcations 323
Reference 333
5 Nonlinear-Bivariate Quadratic Systems 334
5.1 Linear-Bivariate and Nonlinear-Bivariate Vector Fields 334
5.2 Nonlinear-Bivariate Quadratic Systems 363
5.2.1 With a Constant Vector Field 363
5.2.2 With a Linear-Bivariate Linear Vector Field 373
5.2.3 With a Two-Linear-Bivariate-Product Vector Field 381
5.3 Nonlinear and Single-Linear-Bivariate-Quadratic Vector Fields 385
5.4 Nonlinear and Single-Linear-Bivariate-Quadratic Dynamics 407
5.4.1 Saddle-Focus Bifurcations 407
5.4.2 Simple Equilibriums and Switching Bifurcations 415
5.5 Two Nonlinear Bivariate Quadratic Vector Fields 416
5.6 Nonlinear Bivariate Quadratic Dynamics 434
Reference 449
Index 450
备用描述
Such a two-dimensional dynamical system is one of simplest dynamical systems in nonlinear dynamics, but the local and global structures of equilibriums and flows in such two-dimensional quadratic systems help us understand other nonlinear dynamical systems, which is also a crucial step toward solving the Hilbert’s sixteenth problem.
备用描述
Nonlinear Physical Science
Erscheinungsdatum: 21.04.2023
备用描述
Nonlinear Physical Science
Erscheinungsdatum: 30.03.2022
开源日期
2022-06-13
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