On the Periodic Solution Process to the Stochastic Model of Single Species

where N is the population density, b and c are positive numbers, b/c is called carrying capacity. N = 0 and N = b/c are equilibrium points of (1.1). The second of them is more important for us as it is asymptotically stable, i.e. every solution with initial value N(0) O tends to b/c as t+. la [5], the author discussed (1.1) with periodic coefficients and obtained a sufficient condition for the existence of a unique periodic solution. In general, the environment where a population lives in possesses random property. In [4], May considered the random environment with a stochastic differential equation model. About this model some valuable remarks were given by [6]. We start out from May's idea (also see [31) and consider the following stochastic population models