  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.
