Cubic Dynamical Systems, Vol VIII: Two-Dimensional Product-Cubic Systems Crossing-Quadratic Vector Fields

Luo, Albert C. J.

Cubic Dynamical Systems, Vol VIII: Two-Dimensional Product-Cubic Systems Crossing-Quadratic Vector Fields
  • 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: 191
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031571037
  • ISBN-13: 9783031571039

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商品描述

This book, the eighth of 15 related monographs, discusses a product-cubic dynamical system possessing a product-cubic vector field and a crossing-univariate quadratic vector field. It presents equilibrium singularity and bifurcation dynamics, and . the saddle-source (sink) examined is the appearing bifurcations for saddle and source (sink). The double-inflection saddle equilibriums are the appearing bifurcations of the saddle and center, and also the appearing bifurcations of the network of saddles and centers. The infinite-equilibriums for the switching bifurcations featured in this volume include:

  • Parabola-source (sink) infinite-equilibriums,
  • Inflection-source (sink) infinite-equilibriums,
  • Hyperbolic (circular) sink-to source infinite-equilibriums,
  • Hyperbolic (circular) lower-to-upper saddle infinite-equilibriums.

商品描述(中文翻譯)

本書是15本相關專著中的第八本，討論了一個具有產品立方動態系統的產品立方向量場和一個交叉單變量二次向量場。它介紹了平衡奇異性和分歧動態，以及鞍點-源（或決定性點）的出現分歧。雙拐點鞍點平衡是鞍點和中心的出現分歧，也是鞍點和中心網絡的出現分歧。本卷中特色的切換分歧的無窮平衡包括：
- 抛物線源（或決定性點）無窮平衡，
- 拐點源（或決定性點）無窮平衡，
- 雙曲線（或圓形）決定性點到源（或決定性點）無窮平衡，
- 雙曲線（或圓形）下到上鞍點無窮平衡。

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。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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