Abstract
A logistic delay equation with diffusion, which is important in applications, is studied. It is assumed that all of its coefficients, as well as the coefficients in the boundary conditions, are rapidly oscillating functions of time. An averaged equation is constructed, and the relation between its solutions and the solutions of the original equation is studied. A result on the stability of the solutions is formulated, and the problem of local dynamics in the critical case is studied. An algorithm for constructing the asymptotics of the solutions and an algorithm for studying their stability are proposed. It is important to note that the corresponding algorithm contains both a regular and a boundary layer component. Meaningful examples are given.
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Funding
This work was supported by the Russian Foundation for Basic Research under grant 18-29-10043 and by the Ministry of Science and Higher Education of the Russian Federation (project RNOMTs no. 1.13560.2019/13.1).
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Kashchenko, S.A., Loginov, D.O. Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients. Math Notes 108, 50–63 (2020). https://doi.org/10.1134/S0001434620070056
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DOI: https://doi.org/10.1134/S0001434620070056