The structure of a neighborhood of a homogeneous cycle in a medium with diffusion

On the basis of the Krylov–Bogolyubov–Mitropol'skii asymptotic method a technique is developed for constructing a normal form in a neighborhood of a homogeneous cycle of a boundary value problem of “reaction-diffusion” type which loses stability as some parameters change. Its applications are illustrated with a number of substantial examples. In particular, dynamic effects connected with the generation of a cycle from a densification of trajectories are considered.
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