Two-Dimensional Product Cubic Systems, Vol. VII: Self- Quadratic Vector Fields (二維產品立方體系，第七卷：自二次向量場)

Luo, Albert C. J.

Two-Dimensional Product Cubic Systems, Vol. VII: Self- Quadratic Vector Fields
  • 出版商: Springer
  • 出版日期: 2024-10-22
  • 售價: $6,560
  • 貴賓價: 9.5 折 $6,232
  • 語言: 英文
  • 頁數: 232
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031484827
  • ISBN-13: 9783031484827

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

This book is the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include:

- inflection-saddle infinite-equilibriums,

- hyperbolic-source (sink) infinite-equilibriums,

- up-down (down-up) saddle infinite-equilibriums,

- inflection-source (sink) infinite-equilibriums.

商品描述(中文翻譯)

本書是15本相關專著中的第七本，探討具有乘積立方向量場和自變量二次向量場的立方動力系統的非線性動力學和奇異性。討論了平衡奇異性和分岔動力學。鞍源（匯）是鞍和源（匯）出現的分岔。雙鞍平衡是鞍源和鞍匯的出現分岔，也是鞍、匯和源網絡的出現分岔。切換分岔的無限平衡包括：

- 反曲鞍無限平衡，
- 雙曲源（匯）無限平衡，
- 上下（下上）鞍無限平衡，
- 反曲源（匯）無限平衡。

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。Luo 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幾個領域：(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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