TY - JOUR

T1 - Stochastic oscillator with random mass

T2 - New type of Brownian motion

AU - Gitterman, M.

PY - 2014/2/1

Y1 - 2014/2/1

N2 - The model of a stochastic oscillator subject to additive random force, which includes the Brownian motion, is widely used for analysis of different phenomena in physics, chemistry, biology, economics and social science. As a rule, by the appropriate choice of units one assumes that the particle's mass is equal to unity. However, for the case of an additional multiplicative random force, the situation is more complicated. As we show in this review article, for the cases of random frequency or random damping, the mass cannot be excluded from the equations of motion, and, for example, besides the restriction of the size of Brownian particle, some restrictions exist also of its mass. In addition to these two types of multiplicative forces, we consider the random mass, which describes, among others, the Brownian motion with adhesion. The fluctuations of mass are modeled as a dichotomous noise, and the first two moments of coordinates show non-monotonic dependence on the parameters of oscillator and noise. In the presence of an additional periodic force an oscillator with random mass is characterized by the stochastic resonance phenomenon, when the appearance of noise increases the input signal.

AB - The model of a stochastic oscillator subject to additive random force, which includes the Brownian motion, is widely used for analysis of different phenomena in physics, chemistry, biology, economics and social science. As a rule, by the appropriate choice of units one assumes that the particle's mass is equal to unity. However, for the case of an additional multiplicative random force, the situation is more complicated. As we show in this review article, for the cases of random frequency or random damping, the mass cannot be excluded from the equations of motion, and, for example, besides the restriction of the size of Brownian particle, some restrictions exist also of its mass. In addition to these two types of multiplicative forces, we consider the random mass, which describes, among others, the Brownian motion with adhesion. The fluctuations of mass are modeled as a dichotomous noise, and the first two moments of coordinates show non-monotonic dependence on the parameters of oscillator and noise. In the presence of an additional periodic force an oscillator with random mass is characterized by the stochastic resonance phenomenon, when the appearance of noise increases the input signal.

KW - Random mass

KW - Stability conditions

KW - Stochastic oscillator

KW - Stochastic resonance

UR - http://www.scopus.com/inward/record.url?scp=84889880949&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2013.10.020

DO - 10.1016/j.physa.2013.10.020

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SN - 0378-4371

VL - 395

SP - 11

EP - 21

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -