Contents -- Preface -- 1. Formulation of the Problem -- 1.1 Mathematical pendulum -- 1.2 Isomorphicmodels -- 1.2.1 Brownian motion in a periodic potential -- 1.2.2 Josephson junction -- 1.2.3 Fluxon motion in superconductors -- 1.2.4 Charge density waves (CDWs) -- 1.2.5 Laser gyroscope -- 1.2.6 Synchronization phenomena -- 1.2.7 Parametric resonance in anisotropic systems -- 1.2.8 The Frenkel-Kontorova model (FK) -- 1.2.9 Solitons in optical lattices -- 1.3 Noise -- 1.3.1 White noise and colored noise -- 1.3.2 Dichotomous noise -- 1.3.3 Langevin and Fokker-Planck equations -- 2. Overdamped Pendulum -- 2.1 Deterministic motion -- 2.2 Influence of noise -- 2.2.1 Additive white noise -- 2.2.2 Additive and multiplicative white noise -- 2.2.3 Additive dichotomous noise -- 2.2.4 Multiplicative dichotomous noise -- 2.2.5 Joint action of multiplicative noise and additive noise -- 2.2.6 Correlated additive noise and multiplicative noise -- 2.3 Periodic driven force -- 2.3.1 Deterministic equation -- 2.3.2 Influence of noise -- 2.3.3 Deterministic telegraph signal -- 3. Underdamped Pendulum -- 3.1 Pendulum with constant torque -- 3.2 Pendulum with multiplicative noise -- 3.3 Pendulum with additive noise -- 3.3.1 Damped pendulum subject to additive noise -- 3.3.2 Damped pendulum subject to constant torque and noise -- 3.4 Periodically driven pendulum -- 3.5 Damped pendulum subject to constant torque, periodic force and noise -- 3.6 Pendulum with oscillating suspension point -- 3.6.1 Vertical oscillations -- 3.6.2 Horizontal oscillations -- 3.6.3 Pendulum with parametric damping -- 3.7 Spring pendulum -- 3.8 Resonance-type phenomena -- 3.8.1 Stochastic resonance (SR) -- 3.8.2 Absolute negative mobility (ANM) -- 3.8.3 Ratchets -- 3.8.4 Resonance activation (RA) and noise enhanced stability (NES) -- 4. Deterministic Chaos -- 4.1 General concepts.

4.1.1 Poincare sections and strange attractors -- 4.1.2 Lyapunov exponent -- 4.1.3 Correlation function -- 4.1.4 Spectral analysis -- 4.1.5 Period doubling and intermittency -- 4.2 Transition to chaos -- 4.2.1 Damped, periodically driven pendulum -- 4.2.2 Driven pendulum subject to a periodic and constant torque -- 4.2.3 Pendulum with vertically oscillating suspension point -- 4.2.4 Pendulum with horizontally oscillating suspension point -- 4.2.5 Pendulum with applied periodic force -- 4.2.6 Spring pendulum -- 4.3 Pendulum subject to two periodic fields -- 4.3.1 Controlling chaos -- 4.3.2 Erraticmotion -- 4.3.3 Vibrational resonance -- 5. Inverted Pendulum -- 5.1 Oscillations of the suspension axis -- 5.2 The tilted parametric pendulum -- 5.3 Random vibrations of the suspension axis -- 5.4 Spring pendulum -- 5.5 Spring pendulum driven by a periodic force -- 6. Conclusions -- Bibliography -- Index.