不连续动力系统 英文版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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Chapter 1 Introduction1

1.1．A brief history2

1.2．Book layout3

References6

Chapter 2 Introduction to Flow Passability9

2.1．Domain accessibility9

2.2．Discontinuous dynamical systems11

2.3．Flow passability12

2.4．Grazing flows22

2.5．Switching bifurcations of passable flows31

2.6．Switching bifurcations of non-passable flows44

2.7．An application：A frictional oscillator56

2.7.1．Grazing phenomena59

2.7.2．Sliding motion66

References76

Chapter 3 Singularity and Flow Passability77

3.1．Real and imaginary flows77

3.2．G-functions and vector field decomposition82

3.3．Passable flows91

3.4 Non-passable flows99

3.5．Grazing flows114

3.6．Flow switching bifurcations130

3.7．First integral quantity increments150

3.8．An example152

3.8.1．Conditions for sliding and grazing153

3.8.2．Periodic motions156

3.9．Concluding remarks164

References164

Chapter 4 Flow Barriers and Switchability165

4.1．Flow barriers for passable flows165

4.1.1．Coming flow barriers167

4.1.2．Leaving flow barriers183

4.1.3．Passable flows with both flow barriers190

4.2．Flow barriers for sink flows199

4.3．Flow barriers for source flows211

4.3.1．Boundary flow barriers212

4.3.2．Leaving flow barriers226

4.4．Sink flows with flow barriers238

4.5．An application242

4.5.1．Switchability conditions244

4.5.2．Illustrations250

4.6．Concluding remarks257

References258

Chapter 5 Transport Laws and Multi-valued Vector Fields259

5.1．Discontinuity classification259

5.2．Singular sets on boundary262

5.3．Forbidden boundary and boundary channels290

5.3.1．Forbidden boundary290

5.3.2．Boundary channels292

5.4．Domain and boundary classifications298

5.4.1．Domain classification301

5.4.2．Boundary classifications319

5.5．Transport laws325

5.6．Multi-valued vector fields and bouncing flows333

5.6.1．Bouncing flows336

5.6.2．Extended passable flows340

5.7．A controlled piecewise linear system345

5.7.1．Passable and bouncing conditions345

5.7.2．Illustrations351

References356

Chapter 6 Switchability and Attractivity of Domain Flows357

6.1．Dynamical systems on edges357

6.2．Edge classification and mirror domains363

6.3．Domain flow properties to convex edges370

6.4．Domain flow switchability to convex edges377

6.5．Transverse grazing passability to concave edges389

6.6．Domains flow attractivity403

6.6.1．Attractivity to boundary404

6.6.2．Attractivity to edge412

6.7．Multi-valued vector fields switching at edges432

6.7.1．Bouncing domain flows at edges434

6.7.2．Extended passable domain flows to edges442

References446

Chapter 7 Dynamics and Singularity of Boundary Flows447

7.1．Boundary flow properties447

7.2．Boundary flow switchability455

7.3．Switchability of boundary and domain flows480

7.4．Boundary flow attractivity504

7.5．Boundary dynamics with multi-valued vector fields509

7.5.1．Bouncingboundary flows513

7.5.2．Extended passable boundary flows518

References520

Chapter 8 Edge Dynamics and Switching Complexity521

8.1．Edge flows521

8.2．Edge flow switchability529

8.3．Edge flow attractivity551

8.4．Edge dynamics with multi-valued vector fields576

8.4.1．Bouncing edge flows580

8.4.2．Extended passable edge flows588

8.5．A frictional oscillator with two-degrees of freedom594

8.5.1．Domains,edges and vector fields596

8.5.2．Analytical conditions599

8.5.3．Mapping structures and numerical illustrations608

References622

Chapter 9 Dynamical System Interactions623

9.1．Introduction to system interactions623

9.1.1．System interactions623

9.1.2．Discontinuous description625

9.1.3．Resultant dynamical systems629

9.2．Fundamental interactions633

9.3．Interactions with singularity641

9.4．Interactions at edges645

9.5．Application to system synchronization649

9.5.1．Discontinuous description650

9.5.2．Flow switchability on boundaries654

9.5.3．Synchronization invariant sets and mechanism658

9.5.4．Illustrations for synchronization661

References683

Subject Index685