| Preface |
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1 | (26) |
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1.1 Mathematical pendulum |
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1 | (4) |
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1.2 Period of oscillations |
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5 | (5) |
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10 | (5) |
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1.4 Nonlinear vs linear equation |
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15 | (1) |
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16 | (4) |
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1.5.1 Brownian motion in a periodic potential |
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16 | (1) |
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16 | (1) |
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1.5.3 Fluxon motion in superconductors |
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17 | (1) |
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1.5.4 Charge density waves |
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17 | (1) |
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18 | (1) |
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1.5.6 Synchronization phenomena |
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18 | (1) |
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1.5.7 Parametric resonance in anisotropic systems |
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18 | (1) |
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19 | (1) |
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1.5.9 Dynamics of adatom subject to a time-periodic force |
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19 | (1) |
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1.5.10 The Frenkel-Kontorova model (FK) |
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19 | (1) |
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1.5.11 Solitons in optical lattices |
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20 | (1) |
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1.5.12 Other applications |
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20 | (1) |
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20 | (7) |
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21 | (1) |
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1.6.2 Poincare sections and strange attractors |
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21 | (1) |
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22 | (1) |
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1.6.4 Correlation function |
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22 | (1) |
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22 | (1) |
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1.6.6 Period doubling and intermittency |
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23 | (4) |
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27 | (50) |
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2.1 Damped, periodically driven pendulum |
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27 | (14) |
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2.1.1 Transition to chaos |
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27 | (5) |
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2.1.2 Two external periodic fields |
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32 | (2) |
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2.1.3 Dependence on driving frequency |
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34 | (1) |
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35 | (1) |
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36 | (3) |
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2.1.6 Diffusion in a chaotic pendulum |
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39 | (2) |
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41 | (7) |
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2.2.1 Period-doubling bifurcations |
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42 | (3) |
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45 | (3) |
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2.3 Parametric periodic force |
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48 | (14) |
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2.3.1 Pendulum with vertically oscillating suspension point |
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49 | (1) |
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2.3.2 Transition to chaos |
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49 | (2) |
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51 | (1) |
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2.3.4 Parametric periodic non-harmonic force |
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52 | (3) |
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2.3.5 Downward and upward equilibrium configurations |
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55 | (1) |
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2.3.6 Boundary between locked and running solutions |
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56 | (2) |
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2.3.7 Pendulum with horizontally oscillating suspension point |
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58 | (4) |
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2.3.8 Pendulum with both vertical and horizontal oscillations of the suspension point |
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62 | (1) |
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2.4 Parametrically driven pendulum |
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62 | (3) |
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2.5 Periodic and constant forces |
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65 | (4) |
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66 | (3) |
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2.6 Parametric and constant forces |
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69 | (4) |
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2.6.1 Harmonic balance method |
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70 | (1) |
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2.6.2 Heteroclinic and homoclinic trajectories |
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71 | (1) |
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2.6.3 Numerical calculations |
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72 | (1) |
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2.7 External and parametric periodic forces |
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73 | (4) |
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3 Pendulum subject to a Random Force |
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77 | (36) |
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77 | (4) |
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3.1.1 White noise and colored noise |
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77 | (1) |
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78 | (1) |
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3.1.3 Langevin and Fokker-Planck equations |
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79 | (2) |
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3.2 External random force |
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81 | (1) |
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3.3 Constant and random forces |
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82 | (3) |
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3.4 External periodic and random forces |
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85 | (4) |
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3.4.1 Two sources of noise |
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85 | (1) |
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3.4.2 Fokker-Planck equation |
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86 | (1) |
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86 | (2) |
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3.4.4 Absolute negative mobility |
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88 | (1) |
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3.5 Pendulum with multiplicative noise |
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89 | (2) |
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3.6 Parametric periodic and random forces |
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91 | (1) |
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3.7 Damped pendulum subject to a constant torque, periodic force and noise |
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92 | (1) |
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93 | (20) |
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3.8.1 Additive white noise |
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94 | (2) |
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3.8.2 Additive dichotomous noise |
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96 | (3) |
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3.8.3 Multiplicative dichotomous noise |
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99 | (3) |
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3.8.4 Additive and multiplicative white noise |
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102 | (7) |
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3.8.5 Multiplicative dichotomous noise and additive white noise |
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109 | (1) |
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3.8.6 Correlated additive noise and multiplicative noise |
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110 | (3) |
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4 Systems with Two Degrees of Freedom |
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113 | (18) |
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113 | (10) |
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114 | (4) |
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4.1.2 Chaotic behavior of a spring pendulum |
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118 | (2) |
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4.1.3 Driven spring pendulum |
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120 | (3) |
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123 | (3) |
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126 | (5) |
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131 | (2) |
| Bibliography |
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133 | (6) |
| Glossary |
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139 | (2) |
| Index |
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141 | |
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