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The well-known predator-prey model is modified in two ways. First, the regular adding or regular deleting of preys or/and predators is considered. The steady-state and stability diagram are found. Second, random fluctuations of the birthrate and other kinetic coefficients are studied, and the parabolic law of a random walk in the (X,Y)-space is found and proved for small deviations from the steady state.

"Predator and prey" model revisited - influence of external fluxes and noise