Geodesic
The diffusion-buffer phenomenon in a~mathematical model of biology
Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 985-1012

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We consider the Neumann problem for partial differential-difference equations with diffusion that models a predator-prey problem. Using infinite-dimensional normalization, we establish the diffusion-buffer phenomenon, which means that the system can have any number of stable spatially inhomogeneous cycles if its parameters are properly chosen. 
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     title = {The diffusion-buffer phenomenon in a~mathematical model of biology},
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A. Yu. Kolesov; N. Kh. Rozov. The diffusion-buffer phenomenon in a~mathematical model of biology. Izvestiya. Mathematics , Tome 62 (1998) no. 5, pp. 985-1012. http://geodesic.mathdoc.fr/item/IM2_1998_62_5_a5/