Two-Dimensional Crossing-Variable Cubic Nonlinear Systems, Vol IV
Luo, Albert C. J.
- 出版商: Springer
- 出版日期: 2025-01-20
- 售價: $7,030
- 貴賓價: 9.5 折 $6,679
- 語言: 英文
- 頁數: 277
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031628098
- ISBN-13: 9783031628092
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商品描述
This book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+: UP+)-saddle and (3rdUP-: UP-)-saddle) and third-order centers (i.e., (3rd DP+: DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist.
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本相關專著中的第四本，系統地介紹了交叉三次非線性系統的理論。在這個研究中，至少有一個向量場是交叉三次的，而另一個向量場可以是常數、交叉一次、交叉二次和交叉三次的。對於常數向量場，動力系統具有一維流，例如拋物線流和拋物線流加上三次拋物線流。對於交叉一次和交叉三次系統，動力系統具有鞍點和中心平衡、拋物線鞍點、三次中心和鞍點（即（3rd UP +：UP +）-鞍點和（3rdUP-：UP-）-鞍點）以及三次中心（即（3rd DP +：DP-）-中心，（3rd DP-，DP +）-中心）。對於交叉二次和交叉三次系統，除了第一和第三次鞍點和中心以及拋物線鞍點外，還存在（3:2）拋物線鞍點和雙拋物線鞍點，而對於兩個交叉三次系統，存在（3:3）-鞍點和中心。最後，可以形成帶有中心的同宿軌道，並且存在相應的中心和鞍點的同宿網絡。
讀者將學習新的概念、理論、現象和分析技術，包括：
- 常數和交叉三次系統
- 交叉一次和交叉三次系統
- 交叉二次和交叉三次系統
- 交叉三次和交叉三次系統
- 出現和切換分歧
- 三次中心和鞍點
- 拋物線鞍點和拋物線鞍點
- 帶有中心的同宿軌道網絡
- 出現的分歧
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)
Dr. Albert C. J. Luo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。Dr. Luo的研究領域包括非線性力學、非線性動力學和應用數學。他提出並系統地發展了以下理論：(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準確理論，(v) 非線性動力系統穩定性和分歧的新理論。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問題和其他非線性物理問題。這些主要結果散佈在Springer、Wiley、Elsevier和World Scientific的45本專著、200多篇知名期刊論文和150多篇同行評審的會議論文中。
