Two-Dimensional Single-Variable Cubic Nonlinear Systems, Vol II: A Crossingvariable Cubic Vector Field
暫譯: 二維單變量立方非線性系統，第二卷：交叉變量立方向量場
Luo, Albert C. J.
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，系統性地介紹了單變量向量場的三次非線性系統理論。三次向量場是交叉變量，這部分在第二章中討論。書中探討了這些三次系統中的一維流動奇異性和分岔現象。首次呈現了這些二維三次系統中一維流動的出現和切換分岔。書中介紹了三階拋物線流動，以及上鞍流和下鞍流。無限平衡是三階拋物線流動的切換分岔，並且包括第一源和匯流的拐點流，以及上鞍流和下鞍流。在這些三次系統中出現的分岔包括拐點流和三階拋物線流動，上鞍流和下鞍流。
讀者將學習到新的概念、理論、現象和分析技術，包括：
- 常數和交叉三次系統
- 交叉線性和交叉三次系統
- 交叉二次和交叉三次系統
- 交叉三次和交叉三次系統
- 出現和切換分岔
- 三階中心和鞍點
- 拋物線鞍點和拐點鞍點
- 具有中心的同宿軌道網絡
- 出現的分岔
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)
阿爾伯特·C·J·羅博士是美國伊利諾伊州愛德華斯維爾南伊利諾伊大學的傑出研究教授。羅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理論：(i) 不連續動態系統理論，(ii) 非線性動態系統中週期運動的解析解，(iii) 動態系統同步理論，(iv) 非線性可變形體動力學的精確理論，(v) 非線性動態系統的穩定性和分岔的新理論。他在非線性動態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，超過200篇知名期刊論文，以及超過150篇經過同行評審的會議論文。
