Description
Book SynopsisPresents an approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. This title covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics.
Table of ContentsPreface ix
1 Introduction 1
1.1 Brief History 1
1.2 Book Layout 4
2 Nonlinear Dynamical Systems 7
2.1 Continuous Systems 7
2.2 Equilibriums and Stability 9
2.3 Bifurcation and Stability Switching 17
2.3.1 Stability and Switching 17
2.3.2 Bifurcations 26
3 An Analytical Method for Periodic Flows 33
3.1 Nonlinear Dynamical Systems 33
3.1.1 Autonomous Nonlinear Systems 33
3.1.2 Non-Autonomous Nonlinear Systems 44
3.2 Nonlinear Vibration Systems 48
3.2.1 Free Vibration Systems 48
3.2.2 Periodically Excited Vibration Systems 61
3.3 Time-Delayed Nonlinear Systems 66
3.3.1 Autonomous Time-Delayed Nonlinear Systems 66
3.3.2 Non-Autonomous Time-Delayed Nonlinear Systems 80
3.4 Time-Delayed, Nonlinear Vibration Systems 85
3.4.1 Time-Delayed, Free Vibration Systems 85
3.4.2 Periodically Excited Vibration Systems with Time-Delay 102
4 Analytical Periodic to Quasi-Periodic Flows 109
4.1 Nonlinear Dynamical Systems 109
4.2 Nonlinear Vibration Systems 124
4.3 Time-Delayed Nonlinear Systems 134
4.4 Time-Delayed, Nonlinear Vibration Systems 147
5 Quadratic Nonlinear Oscillators 161
5.1 Period-1 Motions 161
5.1.1 Analytical Solutions 161
5.1.2 Frequency-Amplitude Characteristics 165
5.1.3 Numerical Illustrations 173
5.2 Period-m Motions 180
5.2.1 Analytical Solutions 180
5.2.2 Analytical Bifurcation Trees 184
5.2.3 Numerical Illustrations 206
5.3 Arbitrary Periodical Forcing 217
6 Time-Delayed Nonlinear Oscillators 219
6.1 Analytical Solutions 219
6.2 Analytical Bifurcation Trees 238
6.3 Illustrations of Periodic Motions 242
References 253
Index 257
