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This paper presents the explicit form of positive global solution to stochastically perturbed nonautonomous logistic equation where w(t) is the standard one-dimensional Wiener process,ν(t, A) = ν(t, A) − tΠ(A), ν(t, A) is the Poisson measure, which is independent on w(t), E[ν(t, A)] = tΠ(A), Π(A) is a finite measure on the Borel sets in R. If coefficients a(t), b(t), α(t) and γ(t, z) are continuous on t, T -periodic on t functions, a(t) > 0, b(t) > 0 andthen there exists unique, positive T -periodic solution to equation for E[1/N (t)].

It is investigated the non-autonomous logistic differential equation with disturbance of coeffcients by white noise, centered and non-centered Poisson noises. The coeffcients of equation are locally Lipschitz continuous but do not satisfy the linear growth condition. This equation describes the dynamics of population in the Verhulst model which takes into account the logistic eect: an increase of the population size produces a fertility decrease and a mortality increase; since resources are limited, if the population size exceeds some threshold level, the habitat cannot support the growth. The property of stochastic permanence is desirable since it means the long time survival in a population dynamics. The suffcient conditions for the stochastic permanence of population in the considered model is obtained.