ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
The stochastic Verhulst equation has been treated analytically in a perturbation method to obtain approximate expressions for the average value of the population with an arbitrary initial values up to the first order of the noise strength, and to calculate moments with an initial value at the saturation value up to the second order of the noise strength. In calculating the latter, we have transformed the Fokker–Planck equation arising from the stochastic Verhulst equation to that corresponding to the Brownian motion of a particle with a nonlinear potential after introducing a variable. Moreover, we have calculated the mean square displacement for the Brownian particle. The analytical results are compared with the numerical ones, and they are in good agreement for small values of the noise strength.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.452506
