Abstract
The problem about local dynamics of the logistic equation with a rapidly oscillating timeperiodic piecewise constant coefficient of delay has been considered. It has been shown that the averaged equation is a logistic equation with two delays. A stability criterion for equilibrium points has been obtained. The dynamical properties of the original equation are considered provided that the critical case of the equilibrium point stability problem has been implemented. It has been found that an increase of delay coefficient oscillation frequency may lead to an unlimited process of steady-mode birth and death.
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