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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)
這本書是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及平衡網絡和一維流。作者解釋了在這些網絡中，平衡點具有源、匯和鞍點，並且有逆時針和順時針的中心，以及正負鞍點，而一維流包括源流和匯流、帶有雙曲線和雙曲線割線的拋物線流。他進一步描述了奇異平衡點是鞍源（匯）和拋物線鞍點，對於出現的分岔，一維奇異流是雙曲線到雙曲線割線的流和拐點源（匯）流，針對一維流出現的分岔，切換分岔基於無限平衡，包括拐點源（匯）、拋物線源（匯）、上下和下上鞍點（上鞍點和下鞍點）、上下（下上）匯到源和源到匯、雙曲線和雙曲線割線鞍點。對於雙重切換分岔，對角拐點上鞍點和下鞍點的無限平衡也被討論。文中展示了具有連接鞍點、源和中心的雙曲線流網絡，並且也說明了具有平行鞍點和中心的雙曲線流網絡。讀者將學習到新的概念、理論、現象和分析技術。
- 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
- 混合平衡和一維流網絡
- 上下和下上鞍點無限平衡
- 上下和下上匯到源無限平衡
- 拐點源（匯）無限平衡
- 對角拐點鞍點無限平衡
- 無限平衡切換分岔
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茲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。
