Cubic Dynamical Systems, Vol. V: Two-Dimensional Cubic Product Systems

Luo, Albert C. J.

Cubic Dynamical Systems, Vol. V: Two-Dimensional Cubic Product Systems
  • 出版商: Springer
  • 出版日期: 2024-10-25
  • 售價: $5,950
  • 貴賓價: 9.5 折 $5,653
  • 語言: 英文
  • 頁數: 200
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303157091X
  • ISBN-13: 9783031570919

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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，系統地介紹了具有恆定和單變量線性向量場的產品立方非線性系統的理論。產品立方向量場是線性和二次不同單變量函數的乘積。首先討論了具有恆定向量場的立方產品系統中的雙曲線和雙曲線割線流，以及具有自身線性和交叉線性向量場的立方產品系統。介紹了連接的雙曲線流和具有雙曲線割線流的鞍點的切換分叉的拐點源（決策點）無窮平衡。同樣介紹了分離的雙曲線流和具有雙曲線割線流和中心的鞍點的切換分叉的拐點決策點源（決策點）無窮平衡。

讀者將學習到新的概念、理論、現象和分析技術，例如恆定和產品立方系統、線性單變量和產品立方系統、雙曲線和雙曲線割線流、連接的雙曲線和雙曲線割線流、分離的雙曲線和雙曲線割線流、拐點源（決策點）無窮平衡和無窮平衡切換分叉。

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。這些主要成果散佈在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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