Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol III

Luo, Albert C. J.

Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol III
  • 出版商: Springer
  • 出版日期: 2024-10-27
  • 售價: $5,950
  • 貴賓價: 9.5 折 $5,653
  • 語言: 英文
  • 頁數: 277
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031571118
  • ISBN-13: 9783031571114

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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，系統地介紹了自獨立三次非線性系統的理論。在這裡，至少有一個向量場是自三次的，而另一個向量場可以是常數、自線性、自二次或自三次的。對於本書中的常數向量場，動力系統具有一維流，例如源、決點和鞍點流，以及三階源和決點流。對於討論的自線性和自三次系統，動力系統具有源、決點和鞍點平衡，鞍源和鞍決點，三階決點和源（即（3rd SI: SI）-決點和（3rd SO: SO）-源）以及三階源（即（3rd SO: SI）-鞍點，（3rd SI, SO）-鞍點）。對於自二次和自三次系統，除了第一和第三階決點、源和鞍點以及鞍源和鞍決點外，還有（3:2）-鞍點-決點和（3:2）-鞍點-源以及雙鞍點。對於兩個自三次系統，存在（3:3）-源、決點和鞍點。最後，作者描述了可以形成沒有中心的同宿軌道，以及相應的源、決點和鞍點的同宿網絡。

讀者將學習到新的概念、理論、現象和分析技術，包括：
- 常數和交叉三次系統
- 交叉線性和交叉三次系統
- 交叉二次和交叉三次系統
- 交叉三次和交叉三次系統
- 出現和切換分歧
- 三階中心和鞍點
- 拋物線鞍點和拐點鞍點
- 帶有中心的同宿軌道網絡
- 出現的分歧

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)

Dr. Albert C. J. Luo是美國伊利諾伊州愛德華茲維爾南伊利諾伊大學的傑出研究教授。Dr. Luo的研究領域包括非線性力學、非線性動力學和應用數學。他提出並系統地發展了以下理論和方法：(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準確理論，(v) 非線性動力系統穩定性和分歧的新理論。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問題和其他非線性物理問題。他的主要成果散佈在Springer、Wiley、Elsevier和World Scientific等出版社的45本專著、200多篇知名期刊論文和150多篇同行評審的會議論文中。

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