Asymptotic solutions of population dynamic equations

An approach is offered to construct the asymptomatics of the solutions on the small parameter in the close neighborhood of the equilibrium condition of the well-known Volterra-Lotka "prey-predator" system and one of its modifications which takes into account the intraspecies competition of preys and limitation of food resources of a predator. On the basis of the formulas obtained, possible dynamic modes of the size of populations of both kinds are analyzed.