Two-Dimensional Self and Product Cubic Systems, Vol. I

Luo, Albert C. J.

Two-Dimensional Self and Product Cubic Systems, Vol. I
  • 出版商: Springer
  • 出版日期: 2025-03-07
  • 售價: $7,030
  • 貴賓價: 9.5 折 $6,679
  • 語言: 英文
  • 頁數: 240
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031595815
  • ISBN-13: 9783031595813

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商品描述

This book is the twelfth of 15 related monographs on Cubic Systems, discusses self and product cubic systems with a self-linear and crossing-quadratic product vector field. Equilibrium series with flow singularity are presented and the corresponding switching bifurcations are discussed. The volume explains how the equilibrium series with connected hyperbolic and hyperbolic-secant flows exist in such cubic systems, and that the corresponding switching bifurcations are obtained through the inflection-source and sink infinite-equilibriums. Finally, the author illustrates how, in such cubic systems, the appearing bifurcations include saddle-source (sink) for equilibriums and inflection-source and sink flows for the connected hyperbolic flows, and the third-order saddle, sink and source are the appearing and switching bifurcations for saddle-source (sink) with saddles, source and sink, and also for saddle, sink and source.

商品描述(中文翻譯)

這本書是關於立方系統的15本相關專著中的第12本，討論了具有自線性和交叉二次產品向量場的自身和產品立方系統。書中介紹了具有流奇異性的平衡序列，並討論了相應的切換分歧。本書解釋了在這樣的立方系統中存在具有連接的雙曲線和雙曲線割餘流的平衡序列，並且通過拐點源和決定源的無窮平衡獲得相應的切換分歧。最後，作者說明了在這樣的立方系統中，出現的分歧包括平衡的鞍點源（決定源）和連接的雙曲線流的拐點源和決定源流，以及鞍點、決定源和決定源的三階鞍點、決定源和決定源的出現和切換分歧。

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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