Доведено iснування iнварiантних торiв автономної параболiчної системи диференцiальних рiвнянь з малою дифузiєю на колi. Вивчено питання iснування та стiйкостi бiжучих хвиль такої системи. Iснування торiв у цiй параболiчнiй системi зводиться до подiбної задачi для звичайних диференцiальних рiвнянь.

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