Geodesic
The structure of a~neighborhood of a~homogeneous cycle in a~medium with diffusion
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 355-372

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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. Bibliography: 28 titles. 
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     title = {The structure of a~neighborhood of a~homogeneous cycle in a~medium with diffusion},
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A. Yu. Kolesov. The structure of a~neighborhood of a~homogeneous cycle in a~medium with diffusion. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 355-372. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a6/