Cubic Dynamical Systems, Vol. V: Two-Dimensional Cubic Product Systems
暫譯: 立方動態系統，第五卷：二維立方乘積系統

Luo, Albert C. J.

Cubic Dynamical Systems, Vol. V: Two-Dimensional Cubic Product Systems
  • 出版商: Springer
  • 出版日期: 2024-11-01
  • 售價: $6,220
  • 貴賓價: 9.5 折 $5,909
  • 語言: 英文
  • 頁數: 200
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303157091X
  • ISBN-13: 9783031570919

    • 海外代購書籍(需單獨結帳)

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商品描述

This book, the fifth of 15 related monographs, presents systematically a theory of product-cubic nonlinear systems with constant and single-variable linear vector fields. The product-cubic vector field is a product of linear and quadratic different univariate functions. The hyperbolic and hyperbolic-secant flows with directrix flows in the cubic product system with a constant vector field are discussed first, and the cubic product systems with self-linear and crossing-linear vector fields are discussed. The inflection-source (sink) infinite equilibriums are presented for the switching bifurcations of a connected hyperbolic flow and saddle with hyperbolic-secant flow and source (sink) for the connected the separated hyperbolic and hyperbolic-secant flows. The inflection-sink and source infinite-equilibriums with parabola-saddles are presented for the switching bifurcations of a separated hyperbolic flow and saddle with a hyperbolic-secant flow and center.

Readers learn new concepts, theory, phenomena, and analysis techniques, such as Constant and product-cubic systems, Linear-univariate and product-cubic systems, Hyperbolic and hyperbolic-secant flows, Connected hyperbolic and hyperbolic-secant flows, Separated hyperbolic and hyperbolic-secant flows, Inflection-source (sink) Infinite-equilibriums and Infinite-equilibrium switching bifurcations.


商品描述(中文翻譯)

這本書是15本相關專著中的第五本，系統性地介紹了具有常數和單變量線性向量場的乘積立方非線性系統的理論。乘積立方向量場是由線性和二次不同的單變量函數的乘積組成。首先討論了在具有常數向量場的立方乘積系統中，雙曲流和雙曲正割流與導線流的關係，接著討論了具有自線性和交叉線性向量場的立方乘積系統。針對連通的雙曲流和鞍點的切換分岔，提出了拐點源（匯）無限平衡的概念，並探討了連通的分離雙曲流和雙曲正割流的源（匯）。此外，針對分離的雙曲流和鞍點的切換分岔，提出了具有拐點匯和源的無限平衡，並且這些平衡與拋物線鞍點相關。

讀者將學習到新的概念、理論、現象和分析技術，例如常數和乘積立方系統、線性單變量和乘積立方系統、雙曲流和雙曲正割流、連通的雙曲流和雙曲正割流、分離的雙曲流和雙曲正割流、拐點源（匯）無限平衡以及無限平衡切換分岔。

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。

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