不連續(xù)動力系統(tǒng)

內(nèi)容概要

　　本書是關(guān)于不連續(xù)動力系統(tǒng)動力學(xué)及其流轉(zhuǎn)換性理論的專著、本專著提供了研究動力系統(tǒng)網(wǎng)絡(luò)動力學(xué)及其行為復(fù)雜性的數(shù)學(xué)基礎(chǔ)。書中介紹的不連續(xù)動力系統(tǒng)中的障礙向量場理論將徹底改變?nèi)藗冊趧恿W(xué)系統(tǒng)中傳統(tǒng)的思維方式；棱上動力學(xué)及其流轉(zhuǎn)換復(fù)雜性理論是人們討論動力學(xué)系統(tǒng)的低維網(wǎng)絡(luò)通道吸引的數(shù)學(xué)基礎(chǔ)；具有多值向量場的流對其邊界、棱和頂點的跳躍流理論給小廠動力系統(tǒng)網(wǎng)絡(luò)的“臺球”理論的數(shù)學(xué)基礎(chǔ)；動力系統(tǒng)的相互作用理論是動力系統(tǒng)網(wǎng)絡(luò)中的普適性原理，并應(yīng)用于動力系統(tǒng)同步。
　　本書可作為應(yīng)用數(shù)學(xué)、物理、力學(xué)及控制領(lǐng)域的大學(xué)師生及科研人員的參考書。

作者簡介

作者：羅朝俊 叢書主編：（瑞典）伊布拉基莫夫 （墨西哥）阿弗萊諾維奇羅朝俊，博士，美國南伊利諾伊大學(xué)教授，非線性動力學(xué)及力學(xué)領(lǐng)域的國際知名學(xué)者和專家。

書籍目錄

chapter 1 introduction
　1.1. a brief history
　1.2. book layout
　references
chapter 2 introduction to flow passability
　2.1. domain accessibility
　2.2. discontinuous dynamical systems
　2.3. flow passability
　2.4. grazing flows
　2.5. switching bifurcations of passable flows
　2.6. switching bifurcations of non-passable flows
　2.7. an application: a frictional oscillator
　2.7.1. grazing phenomena
　2.7.2. sliding motion
　references
chapter 3 singularity and flow passability
　3.1. real and imaginary flows
　3.2. g-functions and vector field decomposition
　3.3. passable flows
　3.4. non-passable flows
　3.5. grazing flows
　3.6. flow switching bifurcations
　3.7. first integral quantity increments
　3.8. an example
　3.8.1. conditions for sliding and grazing
　3.8.2. periodic motions
　3.9. concluding remarks
　references
chapter 4 flow barriers and switchability
　4.1. flow barriers for passable flows
　4.1.1. coming flow barriers
　4.1.2. leaving flow barriers
　4.1.3. passable flows with both flow barriers
　4.2. flow barriers for sink flows
　4.3. flow barriers for source flows
　4.3.1 boundary flow barriers
　4.3.2. leaving flow barriers
　4.4. sink flows with flow barriers
　4.5. an application
　4.5.1. switchability conditions
　4.5.2. illustrations
　4.6. concluding remarks
　references
chapter 5 transport laws and multi-valued vector fields
　5.1. discontinuity classification
　5.2. singular sets on boundary
　5.3. forbidden boundary and boundary channels
　5.3.1. forbidden boundary
　5.3.2. boundary channels
　5.4. domain and boundary classifications
　5.4.1. domain classification
　5.4.2. boundary classifications
　5.5. transport laws
　5.6. multi-valued vector fields and bouncing flows
　5.6.1. bouncing flows
　5.6.2. extended passable flows
　5.7. a controlled piecewise linear system
　5.7.1. passable and bouncing conditions
　5.7.2. illustrations
　references
chapter 6 switchability and attractivity of domain flows
　6.1. dynamical systems on edges
　6.2. edge classification and mirror domains
　6.3. domain flow properties to convex edges
　6.4. domain flow switchability to convex edges
　6.5. transverse grazing passability to concave edges
　6.6. domains flow attractivity
　6.6.1. attractivity to boundary
　6.6.2. attractivity to edge
　6.7. multi-valued vector fields switching at edges
　6.7.1. bouncing domain flows at edges
　6.7.2. extended passable domain flows to edges
　references
chapter 7 dynamics and singularity of boundary flows
　7.1. boundary flow properties
　7.2. boundary flow switchability
　7.3. switchability of boundary and domain flows
　7.4. boundary flow attractivity
　7.5. boundary dynamics with multi-valued vector fields
　7.5.1. bouncing boundary flows
　7.5.2. extended passable boundary flows
　references
chapter 8 edge dynamics and switching complexity
　8.1. edge flows
　8.2. edge flow switchability
　8.3. edge flow attractivity
　8.4. edge dynamics with multi-valued vector fields
　8.4.1. bouncing edge flows
　8.4.2. extended passable edge flows
　8.5. a frictional oscillator with two-degrees of freedom
　8.5.1. domains, edges and vector fields
　8.5.2. analytical conditions
　8.5.3. mapping structures and numerical illustrations
　references
chapter 9 dynamical system interactions
　9.1. introduction to system interactions
　9.1.1. system interactions
　9.1.2. discontinuous description
　9.1.3. resultant dynamical systems
　9.2. fundamental interactions
　9.3. interactions with singularity
　9.4. interactions at edges
　9.5. application to system synchronization
　9.5 1. discontinuous description
　9.5.2. flow switchability on boundaries
　9.5.3. synchronization invariant sets and mechanism
　9.5.4. illustrations for synchronization
　references
　subject index
　

章節(jié)摘錄

版權(quán)頁：插圖：In this Chapter，the passability of a flow to the boundary of two different dynami-cal systems will be presented.The accessible and inaccessible sub-domains will beintroduced first for a theory of discontinuous dynamic systems.0n the accessibledomains.the corresponding dynamic systems will be introduced.The flow orien-tation and singular sets of boundary will be discussed.The passability and tan-gency（grazing）of a flow to the separation boundary between two adjacent acces-sible domains will be presented.and the necessary and sufficient conditions forsuch passability and tangency of the flow to the boundary will be presented.An L-function of flows will be introduced.and the switching bifurcation conditionsfor the flow passability to the boundary will be discussed.Finally.a friction-induced oscillator will be presented as an example.

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《不連續(xù)動力系統(tǒng)(英文版)》是非線性物理科學(xué)系列叢書之一。

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