Preface | p. vii |
Deterministic and random oscillators | p. 1 |
Simple harmonic oscillator | p. 1 |
Damped harmonic oscillator | p. 2 |
Driven harmonic oscillator | p. 2 |
Driven, damped harmonic oscillator | p. 3 |
Nonlinear oscillator in a double-well potential | p. 3 |
Nonlinear oscillator in a single-well potential | p. 4 |
Harmonic oscillator with external noise | p. 4 |
Brownian motion | p. 4 |
Harmonic oscillator with random frequency | p. 5 |
Harmonic oscillator with random damping | p. 6 |
White and colored noise | p. 7 |
Dichotomous noise | p. 8 |
White Poisson noise | p. 9 |
Shot noise | p. 9 |
Brownian motion | p. 11 |
In the beginning | p. 11 |
Fokker-Planck equation | p. 13 |
Additive white noise | p. 13 |
Multiplicative white noise | p. 15 |
Colored noise: unified colored noise approximation (UCNA) | p. 18 |
Brownian motion and anomalous diffusion | p. 19 |
Brownian motion near the critical point | p. 21 |
Overdamped harmonic oscillator with additive noise | p. 25 |
Additive white noise | p. 26 |
Additive noise and periodic force | p. 27 |
Overdamped harmonic oscillator with multiplicative noise | p. 29 |
Multiplicative noise (shift of stable points) | p. 29 |
Multiplicative and additive noises | p. 30 |
Two white noises | p. 31 |
Two correlated white noises | p. 31 |
Two color dichotomous correlated noises | p. 32 |
Multiplicative color noise and periodic signal (stochastic resonance (SR)) | p. 33 |
Stochastic resonance in a overdamped system with signal-modulated noise | p. 37 |
Overdamped single-well oscillator | p. 41 |
Steady state | p. 42 |
White noises | p. 42 |
Multiplicative noise (gene selection) | p. 44 |
Dichotomous noise | p. 45 |
Poisson white noise | p. 46 |
Response to a periodic force (noise-enhanced stability) | p. 47 |
Piece-wise model of a metastable state | p. 51 |
Rectangular potential barrier (stabilization of metastable state) | p. 54 |
Overdamped double-well oscillator | p. 63 |
Steady state | p. 64 |
White noise | p. 64 |
Dichotomous noise | p. 66 |
Eigenfunction expansion of the Fokker-Planck equation | p. 67 |
Matrix continued fraction method | p. 68 |
Mean first-passage time | p. 71 |
Response to a periodic force (stochastic resonance) | p. 73 |
Fluctuating potential barrier (resonance activation) | p. 78 |
Piece-wise linear potential | p. 79 |
Phenomenological model | p. 81 |
Coherent stochastic resonance | p. 82 |
Harmonic oscillator with additive noise | p. 83 |
Internal and external noise | p. 83 |
White and dichotomous noise | p. 84 |
Additive noise and parametric oscillations | p. 86 |
Nonlinear oscillator with additive noise | p. 89 |
Statistical linearization | p. 89 |
Double-well oscillator with additive noise | p. 91 |
Double-well oscillator driven by two periodic fields (vibrational resonance) | p. 92 |
Harmonic oscillator with random frequency | p. 97 |
First moment for the random frequency | p. 97 |
Force-free oscillator | p. 97 |
White noise | p. 97 |
Colored noise | p. 97 |
Driven oscillator | p. 99 |
Second moment for a random frequency | p. 102 |
Maxwell equation with random dielectric constant | p. 104 |
Driven Maxwell equation | p. 107 |
Harmonic oscillator with random damping | p. 109 |
First moment for random damping | p. 109 |
Force-free oscillator | p. 109 |
Driven oscillator | p. 112 |
Second moment for random damping | p. 116 |
Force-free oscillator | p. 120 |
White noise | p. 120 |
Dichotomous noise | p. 120 |
Driven oscillator | p. 120 |
Second moments | p. 121 |
Correlation functions | p. 122 |
Periodically varying damping | p. 123 |
Nonlinear oscillator with multiplicative noise | p. 125 |
Double-well potential (noise induced reentrant transition) | p. 125 |
Duffing oscillator | p. 129 |
Van der Pol oscillator | p. 130 |
In the future... | p. 133 |
Bibliography | p. 135 |
Index | p. 143 |
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