On a generalized Yorke condition for scalar delayed population models

Abstract

For a scalar delayed differential equation (x)overdot(t) = f(t,x(t)), we give sufficient conditions for the global attractivity of its zero solution. Some technical assumptions are imposed to insure boundedness of solutions and attractivity of non-oscillatory solutions. For controlling the behaviour of oscillatory solutions, we require a very general condition of Yorke type, together with a 3/2-condition. The results are particularly interesting when applied to scalar differential equations with delay which have served as models in populations dynamics, and call be written in the general form (x)overdot(t) = (1 + x(t))F(t, x(t)). Applications to several modelss are presented. improving known results in the literature