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

Luo, Albert C. J.

Two-Dimensional Self and Product Cubic Systems, Vol. II
  • 出版商: Springer
  • 出版日期: 2025-01-29
  • 售價: $6,380
  • 貴賓價: 9.5 折 $6,061
  • 語言: 英文
  • 頁數: 227
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031570995
  • ISBN-13: 9783031570995

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商品描述

This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).


商品描述(中文翻譯)

這本書是關於立方動態系統的15本相關專著中的第15本，討論了具有交叉線性和自我二次產品向量場的交叉和產品立方系統。作者討論了一系列奇異平衡和從雙曲線上到雙曲線下的流動，這些流動通過雙曲線上到下的鞍點、拋物線鞍點、圓形和雙曲線上到下的鞍點無窮平衡點進行切換。還討論了一系列簡單平衡和平行雙曲線流動，這些流動通過拐點源（汲水器）和拋物線鞍點無窮平衡點進行切換。介紹了這種交叉和產品立方系統的非線性動力學和奇異性。在這種立方系統中，出現的分歧包括：拋物線鞍點、雙曲線到雙曲線割線流、三階鞍點（中心）和拋物線鞍點（鞍點-中心）。

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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