Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol III
暫譯: 二維單變數立方非線性系統，第三卷
Luo, Albert C. J.
- 出版商: Springer
- 出版日期: 2024-11-08
- 售價: $5,570
- 貴賓價: 9.5 折 $5,292
- 語言: 英文
- 頁數: 277
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031571118
- ISBN-13: 9783031571114
海外代購書籍(需單獨結帳)
商品描述
This book, the third of 15 related monographs, presents systematically a theory of self-independent cubic nonlinear systems. Here, at least one vector field is self-cubic, and the other vector field can be constant, self-linear, self-quadratic, or self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems discussed, the dynamical systems possess source, sink and saddle equilibriums, saddle-source and saddle-sink, third-order sink and source (i.e, (3rd SI: SI)-sink and (3rdSO: SO)-source) and third-order source (i.e., (3rd SO: SI)-saddle, (3rd SI, SO)-saddle) . For self-quadratic and self-cubic systems, in addition to the first and third-order sink, source and saddles plus saddle-source and saddle-sink, there are (3:2)-saddle-sink and (3:2) saddle-source and double-saddles. For the two self-cubic systems, (3:3)-source, sink and saddles exist. Finally, the author describes that homoclinic orbits without centers can be formed, and the corresponding homoclinic networks of source, sink and saddles exists.
Readers will learn new concepts, theory, phenomena, and analytic techniques, including
Constant and crossing-cubic systems
Crossing-linear and crossing-cubic systems
Crossing-quadratic and crossing-cubic systems
Crossing-cubic and crossing-cubic systems
Appearing and switching bifurcations
Third-order centers and saddles
Parabola-saddles and inflection-saddles
Homoclinic-orbit network with centers
Appearing bifurcations
商品描述(中文翻譯)
這本書是15本相關專著中的第三本，系統性地介紹了自獨立立方非線性系統的理論。在這裡，至少有一個向量場是自立方的，而另一個向量場可以是常數、自線性的、自二次的或自立方的。對於本書中的常數向量場，動態系統擁有一維流，如源流、匯流和鞍流，以及三階源流和匯流。對於討論的自線性和自立方系統，動態系統擁有源、匯和鞍的平衡點，鞍源和鞍匯，三階匯和源（即(3rd SI: SI)-匯和(3rd SO: SO)-源）以及三階源（即(3rd SO: SI)-鞍，(3rd SI, SO)-鞍）。對於自二次和自立方系統，除了第一和第三階的匯、源和鞍以及鞍源和鞍匯外，還有(3:2)-鞍匯和(3:2)-鞍源以及雙鞍。對於兩個自立方系統，存在(3:3)-源、匯和鞍。最後，作者描述了可以形成沒有中心的同宿軌道，並且存在相應的源、匯和鞍的同宿網絡。
讀者將學習到新的概念、理論、現象和分析技術，包括：
- 常數和交叉立方系統
- 交叉線性和交叉立方系統
- 交叉二次和交叉立方系統
- 交叉立方和交叉立方系統
- 出現和切換的分岔
- 三階中心和鞍
- 拋物線鞍和拐點鞍
- 帶中心的同宿軌道網絡
- 出現的分岔
作者簡介
Dr. Albert C. J. Luo is a Distinguished Research Professor at the Southern Illinois University Edwardsville, in Edwardsville, IL, USA. Dr. Luo worked on Nonlinear Mechanics, Nonlinear Dynamics, and Applied Mathematics. He proposed and systematically developed: (i) the discontinuous dynamical system theory, (ii) analytical solutions for periodic motions in nonlinear dynamical systems, (iii) the theory of dynamical system synchronization, (iv) the accurate theory of nonlinear deformable-body dynamics, (v) new theories for stability and bifurcations of nonlinear dynamical systems. He discovered new phenomena in nonlinear dynamical systems. His methods and theories can help understanding and solving the Hilbert sixteenth problems and other nonlinear physics problems. The main results were scattered in 45 monographs in Springer, Wiley, Elsevier, and World Scientific, over 200 prestigious journal papers, and over 150 peer-reviewed conference papers.
作者簡介(中文翻譯)
阿爾伯特·C·J·羅博士是美國伊利諾伊州愛德華斯維爾南伊利諾伊大學的傑出研究教授。羅博士專注於非線性力學、非線性動力學和應用數學。他提出並系統性地發展了以下理論：(i) 不連續動力系統理論，(ii) 非線性動力系統中週期運動的解析解，(iii) 動力系統同步理論，(iv) 非線性可變形體動力學的精確理論，(v) 非線性動力系統的穩定性和分岔的新理論。他在非線性動力系統中發現了新的現象。他的方法和理論有助於理解和解決希爾伯特第十六個問題及其他非線性物理問題。主要成果散見於45本專著，發表於Springer、Wiley、Elsevier和World Scientific，並在200多篇著名期刊論文和150多篇經過同行評審的會議論文中發表。
