图书介绍
Continuous Dynamical Systems=连续动力系统 英文版PDF|Epub|txt|kindle电子书版本下载
- 罗朝俊著 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040348194
- 出版时间：2012
- 标注页数：286页
- 文件大小：9MB
- 文件页数：294页
- 主题词：连续动力系统－英文
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图书目录
Chapter 1 Linear Systems and Stability1
1.1 Linear systems with distinct eigenvalues1
1.2 Operator exponentials7
1.3 Linear systems with repeated eigenvalues8
1.4 Nonhomogeneous linear systems18
1.5 Linear systems with periodic coefficients21
1.6 Stability and boundary22
1.7 Lower-dimensional linear systems33
1.7.1 One-dimensional linear systems33
1.7.2 Planar linear systems35
1.7.3 Three-dimensional linear systems41
References53
Chapter 2 Stability Switching and Bifurcation55
2.1 Continuous dynamical systems55
2.2 Equilibriums and stability58
2.3 Bifurcation and stability switching70
2.3.1 Stability and switching76
2.3.2 Bifurcations95
2.3.3 Lyapunov functions and stability106
References106
Chapter 3 Analytical Periodic Flows and Chaos109
3.1 Analytical periodic flows109
3.1.1 Autonomous nonlinear systems109
3.1.2 Periodically forced nonlinear systems117
3.2 Nonlinear vibration systems121
3.2.1 Free vibration systems121
3.2.2 Periodically forced vibration systems131
3.3 A periodically forced Duffing oscillator135
References165
Chapter 4 Global Transversality and Chaos167
4.1 Nonlinear dynamical systems167
4.2 Local and global flows171
4.3 Global transversality176
4.4 Global tangency184
4.5 Perturbed Hamiltonian systems192
4.6 Two-dimensional Hamiltonian systems196
4.7 First integral quantity increment201
4.8 A damped Duffing oscillator204
4.8.1 Conditions for global transversality and tangency206
4.8.2 Poincare mapping and mapping structures211
4.8.3 Bifurcation scenario217
4.8.4 Numerical illustrations223
References236
Chapter 5 Resonance and Hamiltonian Chaos237
5.1 Stochastic layers237
5.1.1 Definitions237
5.1.2 Approximate criteria241
5.2 Resonant separatrix layers250
5.2.1 Layer dynamics252
5.2.2 Approximate criteria257
5.3 A periodically forced Duffing oscillator262
5.3.1 Approximate predictions262
5.3.2 Numerical illustrations269
5.4 Concluding remarks282
References283
Index285