二維二次非線性系統-雙變量向量場Two-Dimensional Quadratic Nonlinear Sys 9787

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書名:二維二次非線性系統-雙變量向量場Two-Dimensional Quadratic Nonlinear Sys
ISBN:9787040602111
出版社:高等教育
著編譯者:AlbertC.J.Luo(羅朝俊
叢書名:非線性物理科學
頁數:445
所在地:中國大陸 *此為代購商品
書號:1595014
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【台灣高等教育出版社簡體書】 二維二次非線性系統-雙變量向量場Two-Dimensional Quadratic Nonlinear Sys 787040602111 AlbertC.J.Luo(羅朝俊

內容簡介

本書的重點是基於向量場和二元二次函數的非線性動力學。本書從不同視角研究非線性動力學和二次動力系統的分岔。二維動力系統是非線性動力學中最簡單的動力系統之一,但二維二次系統中平衡點和流的局部和全局結構有助於我們理解其他非線性動力系統,這也是解決希爾伯特第十六問題的關鍵一步。本書詳細探討了二維二次系統可能存在的奇異動力學問題;介紹了二維繫統中平衡態和一維流的動力學;討論了鞍形匯和鞍形源分岔,給出了鞍形中心分岔;提出了無限平衡態是非線性系統的開關分岔;從第一類積分流形出發,發展了鞍焦點網路,並給出了鞍、源和匯網路。 本書可作為動力系統和控制專業的參考書,適用於數學、機械和電氣工程領域的研究人員、學生和工程師。

作者簡介

羅朝俊教授為非線性動力學和力學領域國際知名學者,美國南伊利諾伊大學傑出研究講席教授,主要研究領域為哈密頓系統混沌、非線性變形體動力學、不連續動力系統、動力系統的穩定性和分岔理論、動力系統的同步與跟蹤理論、動力系統周期運動和混沌的解析解與半解析解、微分方程的解析解與數值解等。

目錄

1 Two-Dimensional Linear-Bivariate Linear Systems
1 1 Single-Linear-Bivariate Linear Systems
1 2 One-Dimensional Flows and Switching Bifurcations
1 3 Two Linear-Bivariate Linear Systems
References
2 Single-Linear-Bivariate Quadratic Systems
2 1 Constant and Linear-Bivariate Quadratic Vector Fields
2 2 Single-Bivariate Linear and Quadratic Vector Fields
2 2 1 Single-Bivariate Linear and Quadratic Systems
2 2 2 Flow Switching and Appearing Bifurcations
2 3 Two Quadratic Vector Fields with a Single-Bivariate Function
2 3 1 A Single-Linear-Bivariate Quadratic System
2 3 2 Appearing and Switching Bifurcations
Reference
3 Linear-Bivariate Quadratic Dynamics
3 1 Linear and Quadratic Linear-Bivariate Vector Fields
3 2 Saddle-Focus and Saddle-Node Bifurcations
3 3 Two Linear-Bivariate Quadratic Vector Fields
3 4 Saddle-Focus Bifurcations and Global Dynamics
3 4 1 Saddle-Focus Appearing and Switching Bifurcations
3 4 2 Focus-Saddle Network
Reference
4 Linear-Bivariate Product Quadratic Systems
4 1 Two Linear-Bivariate Product Quadratic Vector Fields
4 2 Linear-Bivariate-Product Quadratic Systems
4 2 1 With a Constant Vector Field
4 2 2 With a Linear-Bivariate Linear Vector Field
4 2 3 Two Linear-Bivariate Product Quadratic Vector Fields
4 2 4 Switching Bifurcations
4 3 Product and Single Linear-Bivariate Quadratic Vector Fields
4 4 Product and Single Linear-Bivariate Quadratic Dynamics
4 4 1 Saddle-Focus Bifurcations
4 4 2 Simple Equilibriums and Switching Bifurcations
Reference
5 Nonlinear-Bivariate Quadratic Systems
5 1 Linear-Bivariate and Nonlinear-Bivariate Vector Fields
5 2 Nonlinear-Bivariate Quadratic Systems
5 2 1 With a Constant Vector Field
5 2 2 With a Linear-Bivariate Linear Vector Field
5 2 3 With a Two-Linear-Bivariate-Product Vector Field
5 3 Nonlinear and Single-Linear-Bivariate-Quadratic Vector Fields
5 4 Nonlinear and Single-Linear-Bivariate-Quadratic Dynamics
5 4 1 Saddle-Focus Bifurcations
5 4 2 Simple Equilibriums and Switching Bifurcations
5 5 Two Nonlinear Bivariate Quadratic Vector Fields
5 6 Nonlinear Bivariate Ouadratic Dynamics
Reference
Index
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