6533b862fe1ef96bd12c76b8
RESEARCH PRODUCT
Verhulst model with Lévy white noise excitation
Bernardo SpagnoloAlexander A. Dubkovsubject
Physicswhite noise excitationStatistical Mechanics (cond-mat.stat-mech)Shot noiseFOS: Physical sciencesCauchy distributionDirac delta functionProbability density functionWhite noiseCondensed Matter PhysicsNoise (electronics)Lévy processElectronic Optical and Magnetic Materialssymbols.namesakesymbolsProbability distributionStatistical physicsCondensed Matter - Statistical Mechanicsdescription
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Levy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 |