Two-Dimensional Two Product Cubic Systems, Vol. III: Self-Linear and Crossing Quadratic Product Vector Fields
暫譯: 二維二乘立方系統，第三卷：自線性與交叉二次乘積向量場
Luo, Albert C. J.
- 出版商: Springer
- 出版日期: 2024-10-11
- 售價: $6,590
- 貴賓價: 9.5 折 $6,261
- 語言: 英文
- 頁數: 225
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031595580
- ISBN-13: 9783031595585
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相關分類:
微積分 Calculus
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相關主題
商品描述
This book is the eleventh of 15 related monographs on Cubic Systems, examines self-linear and crossing-quadratic product systems. It discusses the equilibrium and flow singularity and bifurcations, The double-inflection saddles featured in this volume are the appearing bifurcations for two connected parabola-saddles, and also for saddles and centers. The parabola saddles are for the appearing bifurcations of saddle and center. The inflection-source and sink flows are the appearing bifurcations for connected hyperbolic and hyperbolic-secant flows. Networks of higher-order equilibriums and flows are presented. For the network switching, the inflection-sink and source infinite-equilibriums exist, and parabola-source and sink infinite-equilibriums are obtained. The equilibrium networks with connected hyperbolic and hyperbolic-secant flows are discussed. The inflection-source and sink infinite-equilibriums are for the switching bifurcation of two equilibrium networks.
商品描述(中文翻譯)
這本書是關於立方系統的15本相關專著中的第十一本，探討自線性和交叉二次乘積系統。它討論了平衡和流動奇異性及分岔。本卷中的雙拐點鞍點是兩個連接的拋物線鞍點出現的分岔，並且也適用於鞍點和中心。拋物線鞍點是鞍點和中心出現的分岔。拐點源和匯流是連接的雙曲流和雙曲割流出現的分岔。書中呈現了高階平衡和流動的網絡。對於網絡切換，存在拐點匯和源的無限平衡，並獲得了拋物線源和匯的無限平衡。討論了具有連接的雙曲流和雙曲割流的平衡網絡。拐點源和匯的無限平衡是兩個平衡網絡的切換分岔。
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篇著名期刊論文，以及超過150篇經過同行評審的會議論文。
