Dynamics of a Delay Logistic Equation with Diffusion and Coefficients Rapidly Oscillating in Space Variable

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The applicability of the averaging principle in the study of the dynamics of a practically important delay logistic equation with diffusion and coefficients rapidly oscillating with respect to the space variable is analyzed. A task of special interest is to address equations with rapid oscillations of the delay coefficient or a quantity characterizing the deviation of the space variable. Bifurcation problems arising in critical cases for the averaged equation are studied. Results concerning the existence, stability, and asymptotic behavior of periodic solutions to the original equation are formulated.