Stochastic oscillator with random mass: New type of Brownian motion

M. Gitterman

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish
Pages (from-to)11-21
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 1 Feb 2014


  • Random mass
  • Stability conditions
  • Stochastic oscillator
  • Stochastic resonance


Dive into the research topics of 'Stochastic oscillator with random mass: New type of Brownian motion'. Together they form a unique fingerprint.

Cite this