Cubic Dynamical Systems, Vol VIII: Two-Dimensional Product-Cubic Systems Crossing-Quadratic Vector Fields
暫譯: 立方動力系統，第八卷：二維乘積立方系統交叉二次向量場
Luo, Albert C. J.
相關主題
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)
這本書是15本相關專著中的第八本，討論了一個擁有乘積立方向量場和交叉單變量二次向量場的乘積立方動力系統。它呈現了平衡奇異性和分岔動力學，並且所檢視的鞍源（匯）是鞍和源（匯）出現的分岔。雙拐點鞍平衡是鞍和中心出現的分岔，並且也是鞍和中心網絡出現的分岔。本卷中所特徵的切換分岔的無限平衡包括：
- 拋物線源（匯）無限平衡，
- 拐點源（匯）無限平衡，
- 雙曲（圓形）匯到源無限平衡，
- 雙曲（圓形）下鞍到上鞍無限平衡。
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)
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精確理論，(v) 非線性動力系統的穩定性和分岔的新理論。他在非線性動力系統中發現了新現象。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，並在200多篇著名期刊論文和150多篇經過同行評審的會議論文中發表。
