Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol VI
Luo, Albert C. J.
- 出版商: Springer
- 出版日期: 2024-11-01
- 售價: $6,280
- 貴賓價: 9.5 折 $5,966
- 語言: 英文
- 頁數: 101
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031571150
- ISBN-13: 9783031571152
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商品描述
This book, the sixth of 15 related monographs, discusses singularity and networks of equilibriums and 1-diemsnional flows in product quadratic and cubic systems. The author explains how, in the networks, equilibriums have source, sink and saddles with counter-clockwise and clockwise centers and positive and negative saddles, and the 1-dimensional flows includes source and sink flows, parabola flows with hyperbolic and hyperbolic-secant flows. He further describes how the singular equilibriums are saddle-source (sink) and parabola-saddles for the appearing bifurcations, and the 1-dimensional singular flows are the hyperbolic-to-hyperbolic-secant flows and inflection source (sink) flows for 1-dimensional flow appearing bifurcations, and the switching bifurcations are based on the infinite-equilibriums, including inflection-source (sink), parabola-source (sink), up-down and down-up upper-saddle (lower-saddle), up-down (down-up) sink-to-source and source-to-sink, hyperbolic and hyperbolic-secant saddles. The diagonal-inflection upper-saddle and lower-saddle infinite-equilibriums are for the double switching bifurcations. The networks of hyperbolic flows with connected saddle, source and center are presented, and the networks of the hyperbolic flows with paralleled saddle and center are also illustrated. Readers will learn new concepts, theory, phenomena, and analysis techniques.
- Product-quadratic and product cubic systems
- Self-linear and crossing-quadratic product vector fields
- Self-quadratic and crossing-linear product vector fields
- Hybrid networks of equilibriums and 1-dimensional flows
- Up-down and down-up saddle infinite-equilibriums
- Up-down and down-up sink-to-source infinite-equilibriums
- Inflection-source (sink) Infinite-equilibriums
- Diagonal inflection saddle infinite-equilibriums
- Infinite-equilibrium switching bifurcations
商品描述(中文翻譯)
本書是15本相關專著中的第六本,討論了產品二次和三次系統中的奇異性和均衡網絡以及一維流動。作者解釋了在這些網絡中,均衡點具有源、決點和鞍點,並且有順時針和逆時針的中心以及正和負的鞍點。一維流動包括源流和決點流、拋物線流動以及雙曲線和雙曲線割餘流。他進一步描述了奇異均衡是出現分歧時的鞍源(決點)和拋物線鞍,一維奇異流動是出現分歧時的雙曲線到雙曲線割餘流和拐點源(決點)流,切換分歧基於無窮均衡,包括拐點源(決點)、拋物線源(決點)、上下和下上的上鞍(下鞍)、上下(下上)決點到源和源到決點、雙曲線和雙曲線割餘鞍。對角拐點上鞍和下鞍無窮均衡用於雙重切換分歧。書中介紹了具有連接鞍、源和中心的雙曲線流動網絡,並且還展示了具有平行鞍和中心的雙曲線流動網絡。讀者將學習到新的概念、理論、現象和分析技巧。
- 產品二次和產品三次系統
- 自線性和交叉二次產品向量場
- 自二次和交叉線性產品向量場
- 均衡和一維流動的混合網絡
- 上下和下上鞍無窮均衡
- 上下和下上決點到源無窮均衡
- 拐點源(決點)無窮均衡
- 對角拐點鞍無窮均衡
- 無窮均衡切換分歧
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。