Two-Dimensional Self and Product Cubic Systems, Vol. I: Crossing-Linear and Self-Quadratic Product Vector Field

Luo, Albert C. J.

Two-Dimensional Self and Product Cubic Systems, Vol. I: Crossing-Linear and Self-Quadratic Product Vector Field
  • 出版商: Springer
  • 出版日期: 2024-10-29
  • 售價: $6,280
  • 貴賓價: 9.5 折 $5,966
  • 語言: 英文
  • 頁數: 111
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031570952
  • ISBN-13: 9783031570957

    • 尚未上市，無法訂購

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商品描述

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:

  • double-inflection saddles,
  • inflection-source (sink) flows,
  • parabola-saddles (saddle-center),
  • third-order parabola-saddles,
  • third-order saddles (centers),
  • third-order saddle-source (sink).

商品描述(中文翻譯)

這本書是關於立方動力系統的15本相關專著中的第14本，討論了具有自線性和交叉二次產品向量場的交叉和乘積立方系統。羅博士討論了具有拋物線源（決點）無窮平衡的拋物線源（決點）流的奇異平衡序列，並與拋物線源（決點）無窮平衡進行切換。他進一步描述了獲得了具有連接的雙曲線流的簡單平衡的網絡，並與拋物線鞍點無窮平衡進行切換，以及這種交叉和乘積立方系統的非線性動力學和奇異性。在這樣的立方系統中，出現的分歧有：

- 雙拋物線鞍點
- 拋物線源（決點）流
- 拋物線鞍點（鞍點-中心）
- 三階拋物線鞍點
- 三階鞍點（中心）
- 三階鞍點源（決點）。

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：(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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