Growth with regulation in fluctuating environments

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Abstract
Population growth is modelled by means of diffusion processes originating from fluctuation equations of a new type. These equations are obtained in the customary way by inserting random fluctuations into first order non linear differential equations. However, differently from the cases so far considered in the literature, equations possessing two non trivial fixed points are taken into account. The underlying deterministic models depict the regulated growth of a population whose size cannot decrease below some preassigned lower threshold naturally acting as an absorbing boundary. A fairly comprehensive mathematical description of these models is provided.