Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossingvariable Cubic Vector Field

Luo, Albert C. J.

Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossingvariable Cubic Vector Field
  • 出版商: Springer
  • 出版日期: 2024-12-21
  • 售價: $6,360
  • 貴賓價: 9.5 折 $6,042
  • 語言: 英文
  • 頁數: 197
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303157107X
  • ISBN-13: 9783031571077

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相關主題

商品描述

This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows.

Readers will learn new concepts, theory, phenomena, and analytic techniques, including
Constant and crossing-cubic systems
Crossing-linear and crossing-cubic systems
Crossing-quadratic and crossing-cubic systems
Crossing-cubic and crossing-cubic systems
Appearing and switching bifurcations
Third-order centers and saddles
Parabola-saddles and inflection-saddles
Homoclinic-orbit network with centers
Appearing bifurcations

商品描述(中文翻譯)

這本書是15本相關專著中的第二本，系統地介紹了具有單變量向量場的立方非線性系統的理論。立方向量場是交叉變量的，這部分在書中作為第二部分進行了討論。書中討論了這種立方系統中的一維流奇異點和分歧。首次介紹了這種二維立方系統中一維流的出現和切換分歧。書中還介紹了三階抛物線流，以及上下鞍點流。無窮均衡是一階和三階抛物線流的切換分歧，以及帶有第一源和第一匯流的拐點流和上下鞍點流。這種立方系統中的出現分歧包括拐點流和三階抛物線流，以及上下鞍點流。

讀者將學習到新的概念、理論、現象和分析技巧，包括：
- 常數和交叉立方系統
- 交叉線性和交叉立方系統
- 交叉二次和交叉立方系統
- 交叉立方和交叉立方系統
- 出現和切換分歧
- 三階中心和鞍點
- 抛物線鞍點和拐點鞍點
- 帶有中心的同宿軌道網絡
- 出現分歧

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。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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