title: Transient and stationary characteristics of the Malthus-Verhulst-Bernoulli model with non-Gaussian fluctuating parameters.
abstract: Two generalized Verhulst equations with non-Gaussian fluctuations of the reproduction rate and the volume of resources are under analytical investigation. For the first model, using the central limit theorem, we find the asymptotic behavior of the probability distribution of population density for an arbitrary non-Gaussian colored noise with nonzero power spectral density at zero frequency. Specifically, we confirm this result in the case of Markovian dichotomous noise and examine the evolution of mean population density. For fluctuating resources with one-sided stable distribution the transient dynamics of probability density function and statistical characteristics in the steady state are obtained. As shown, the scenario of the population's evolution depends on the parameter of nonlinearity in the original stochastic equation.
authors.affiliation: Radiophysics Department, Lobachevsky State University, 23 Gagarin Avenue, 603950 Nizhniy Novgorod, Russia.
authors.forename: Alexander A
authors.initials: AA
authors.lastname: Dubkov
authors.affiliation: Radiophysics Department, Lobachevsky State University, 23 Gagarin Avenue, 603950 Nizhniy Novgorod, Russia.
authors.forename: Anna A
authors.initials: AA
authors.lastname: Kharcheva
mesh_terms: D003198:Computer Simulation; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D016011:Normal Distribution; D013269:Stochastic Processes