Continuous Dynamical Systems=连续动力系统 英文版PDF电子书下载

Chapter 1 Linear Systems and Stability 1

1.1 Linear systems with distinct eigenvalues 1

1.2 Operator exponentials 7

1.3 Linear systems with repeated eigenvalues 8

1.4 Nonhomogeneous linear systems 18

1.5 Linear systems with periodic coefficients 21

1.6 Stability and boundary 22

1.7 Lower-dimensional linear systems 33

1.7.1 One-dimensional linear systems 33

1.7.2 Planar linear systems 35

1.7.3 Three-dimensional linear systems 41

References 53

Chapter 2 Stability Switching and Bifurcation 55

2.1 Continuous dynamical systems 55

2.2 Equilibriums and stability 58

2.3 Bifurcation and stability switching 70

2.3.1 Stability and switching 76

2.3.2 Bifurcations 95

2.3.3 Lyapunov functions and stability 106

References 106

Chapter 3 Analytical Periodic Flows and Chaos 109

3.1 Analytical periodic flows 109

3.1.1 Autonomous nonlinear systems 109

3.1.2 Periodically forced nonlinear systems 117

3.2 Nonlinear vibration systems 121

3.2.1 Free vibration systems 121

3.2.2 Periodically forced vibration systems 131

3.3 A periodically forced Duffing oscillator 135

References 165

Chapter 4 Global Transversality and Chaos 167

4.1 Nonlinear dynamical systems 167

4.2 Local and global flows 171

4.3 Global transversality 176

4.4 Global tangency 184

4.5 Perturbed Hamiltonian systems 192

4.6 Two-dimensional Hamiltonian systems 196

4.7 First integral quantity increment 201

4.8 A damped Duffing oscillator 204

4.8.1 Conditions for global transversality and tangency 206

4.8.2 Poincare mapping and mapping structures 211

4.8.3 Bifurcation scenario 217

4.8.4 Numerical illustrations 223

References 236

Chapter 5 Resonance and Hamiltonian Chaos 237

5.1 Stochastic layers 237

5.1.1 Definitions 237

5.1.2 Approximate criteria 241

5.2 Resonant separatrix layers 250

5.2.1 Layer dynamics 252

5.2.2 Approximate criteria 257

5.3 A periodically forced Duffing oscillator 262

5.3.1 Approximate predictions 262

5.3.2 Numerical illustrations 269

5.4 Concluding remarks 282

References 283

Index 285