相關主題
商品描述
This book, the 15th of 15 related monographs on Cubic Dynamic Systems, discusses crossing and product cubic systems with a crossing-linear and self-quadratic product vector field. The author discusses series of singular equilibriums and hyperbolic-to-hyperbolic-scant flows that are switched through the hyperbolic upper-to-lower saddles and parabola-saddles and circular and hyperbolic upper-to-lower saddles infinite-equilibriums. Series of simple equilibrium and paralleled hyperbolic flows are also discussed, which are switched through inflection-source (sink) and parabola-saddle infinite-equilibriums. Nonlinear dynamics and singularity for such crossing and product cubic systems are presented. In such cubic systems, the appearing bifurcations are: parabola-saddles, hyperbolic-to-hyperbolic-secant flows, third-order saddles (centers) and parabola-saddles (saddle-center).
商品描述(中文翻譯)
這本書是關於立方動態系統的15本相關專著中的第15本，討論了具有交叉線性和自二次乘積向量場的交叉和乘積立方系統。作者探討了一系列奇異平衡和超雙曲到超雙曲稀疏流，這些流通過超雙曲的上到下鞍點、拋物線鞍點以及圓形和超雙曲的上到下鞍點的無限平衡進行切換。還討論了一系列簡單平衡和並行的超雙曲流，這些流通過拐點源（匯）和拋物線鞍點的無限平衡進行切換。書中呈現了這些交叉和乘積立方系統的非線性動力學和奇異性。在這些立方系統中，出現的分岔包括：拋物線鞍點、超雙曲到超雙曲的割流、三階鞍點（中心）和拋物線鞍點（鞍中心）。
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。
