Dynamics of the logistic equation with two delays

Аннотация

We study the logistic equation with two delays. When studying its nonlocal dynamics, we obtain a condition for the existence and the asymptotics of a relaxation cycle. When studying the local dynamics, we show that the behavior of solutions of the original equation is determined by the structure of solutions of special families of nonlinear boundary value problems of parabolic and degenerate-parabolic type.