Two-Dimensional Quadratic Nonlinear Systems: Volume II: Bivariate Vector Fields
暫譯: 二維二次非線性系統：第二卷：雙變量向量場

Luo, Albert C. J.

Two-Dimensional Quadratic Nonlinear Systems: Volume II: Bivariate Vector Fields
  • 出版商: Springer
  • 出版日期: 2026-03-12
  • 售價: $7,150
  • 貴賓價: 9.5 折 $6,792
  • 語言: 英文
  • 頁數: 445
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 9811678715
  • ISBN-13: 9789811678714
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

The book focuses on the nonlinear dynamics based on the vector fields with bivariate quadratic functions. This book is a unique monograph for two-dimensional quadratic nonlinear systems based on bivariate vector fields. Such a book provides different points of view about nonlinear dynamics and bifurcations of the quadratic dynamical systems on linear and nonlinear bivariate manifolds. Possible singular dynamics of the two-dimensional quadratic systems is discussed in detail. The dynamics of equilibriums and one-dimensional flows on bivariate manifolds are presented. Saddle-focus bifurcations are discussed, and switching bifurcations based on infinite-equilibriums are presented. Saddle-focus networks on bivariate manifolds are demonstrated. This book will serve as a reference book on dynamical systems and control for researchers, students and engineering in mathematics, mechanical and electrical engineering.

商品描述(中文翻譯)

本書專注於基於二元二次函數的向量場的非線性動力學。這本書是針對基於二元向量場的二維二次非線性系統的獨特專著。這樣的書籍提供了關於二次動力系統在線性和非線性二元流形上的非線性動力學和分岔的不同觀點。詳細討論了二維二次系統的可能奇異動力學。書中呈現了在二元流形上的平衡點動力學和一維流動。討論了鞍點-焦點分岔，並介紹了基於無限平衡點的切換分岔。展示了在二元流形上的鞍點-焦點網絡。本書將作為動力系統和控制的參考書籍，供數學、機械工程和電氣工程的研究人員、學生和工程師使用。

作者簡介

Prof. Albert C. J. Luo is a Distinguished Research Professor at the Department of Mechanical Engineering at Southern Illinois University Edwardsville, USA. He received his Ph.D. degree from the University of Manitoba, Canada, in 1995. His research focuses on nonlinear dynamics, nonlinear mechanics and nonlinear differential equations, and he has published over 40 books and more than 350 journal articles and conference papers in these fields. He received the Paul Simon Outstanding Scholar Award in 2008 and an ASME fellowship in 2007. He was an editor for Communications in Nonlinear Science and Numerical Simulation, and an associate editor for ASME Journal of Computational and Nonlinear Dynamics. He now serves as Co-editor of the Journal of Applied Nonlinear Dynamics and Editor of various book series, including "Nonlinear Systems and Complexity" and "Nonlinear Physical Science."

His major contributions on nonlinear dynamical systems are:

- A theory for stochastic and resonant layers in nonlinear Hamiltonian systems

- A local theory and singularity for discontinuous dynamical systems

- Flow barriers theory for discontinuous dynamical systems

- Synchronization of continuous dynamical systems under specific constraints

- Synchronization and companion of discrete dynamical systems

- Analytical solutions of periodic motions in nonlinear systems

- Discretization and implicit mapping dynamics in nonlinear dynamical systems

- Periodic flows in time-delay systems

- Memorized nonlinear dynamical systems

In addition, Luo developed accurate theories for nonlinear deformable-body dynamics, machine tool dynamics and others:

- An approximate plate theory

- A theory for soft structures

- A nonlinear theory for beams and rods

- Fluid-induced nonlinear structural vibration

- A large damage theory for anisotropic materials

- A generalized fractal theory

He has published over 350 peer-reviewed journal and conference papers. Luo has been an editor for the Journal Communications in Nonlinear Science and Numerical simulation, and the book series on Nonlinear Systems and Complexity (Springer), and Nonlinear Physical Science (Higher Education Press and Springer).

作者簡介(中文翻譯)

阿爾伯特·C·J·羅教授是美國南伊利諾伊大學愛德華斯維爾機械工程系的傑出研究教授。他於1995年獲得加拿大曼尼托巴大學的博士學位。他的研究專注於非線性動力學、非線性力學和非線性微分方程，並在這些領域發表了超過40本書籍和350篇以上的期刊文章及會議論文。他於2008年獲得保羅·西蒙傑出學者獎，並於2007年獲得ASME獎學金。他曾擔任《非線性科學與數值模擬通訊》的編輯，以及《ASME計算與非線性動力學期刊》的副編輯。目前，他擔任《應用非線性動力學期刊》的共同編輯，以及多個書系的編輯，包括《非線性系統與複雜性》和《非線性物理科學》。

他在非線性動力系統方面的主要貢獻包括：

- 非線性哈密頓系統中的隨機和共振層理論
- 不連續動力系統的局部理論和奇異性
- 不連續動力系統的流動障礙理論
- 在特定約束下的連續動力系統的同步
- 離散動力系統的同步與伴隨
- 非線性系統中週期運動的解析解
- 非線性動力系統中的離散化和隱式映射動力學
- 時延系統中的週期流動
- 記憶型非線性動力系統

此外，羅教授還為非線性可變形體動力學、機械工具動力學等領域開發了準確的理論：

- 近似板理論
- 軟結構的理論
- 梁和桿的非線性理論
- 流體引起的非線性結構振動
- 向異性材料的大損傷理論
- 一般化分形理論

他已發表超過350篇經過同行評審的期刊和會議論文。羅教授曾擔任《非線性科學與數值模擬期刊》的編輯，以及《非線性系統與複雜性》（Springer）和《非線性物理科學》（高等教育出版社和Springer）書系的編輯。

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