- 作 者：罗朝俊著
- 出 版 社：北京：高等教育出版社
- 出版年份：2012
- ISBN：9787040348194
- 标注页数：286 页
- PDF页数：294 页
请阅读订购服务说明与试读!
订购服务说明
1、本站所有的书默认都是PDF格式，该格式图书只能阅读和打印，不能再次编辑。
2、除分上下册或者多册的情况下，一般PDF页数一定要大于标注页数才建议下单购买。【本资源294 ≥286页】
图书下载及付费说明
1、所有的电子图书为PDF格式，支持电脑、手机、平板等各类电子设备阅读；可以任意拷贝文件到不同的阅读设备里进行阅读。
2、电子图书在提交订单后一般半小时内处理完成,最晚48小时内处理完成。(非工作日购买会延迟)
3、所有的电子图书都是原书直接扫描方式制作而成。
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