О динамике бегущих волн в системе уравнений Ван-дер-Поля с малой диффузией

Abstract

The dynamics of traveling waves for a system of parabolic equations of the van-der-Pol type with small diffusion on a circle with radius r is studied. The existence, interaction, asymptotic form, and stability of these waves are analyzed. It is proved that the number of stable traveling waves increases with the radius r, and it is shown that the interaction of the waves satisfies the 1 : 2 principle.