ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Borina M. Y., Polezhaev A. A. Spatial-temporal patterns in a multidimensional active medium formed due to polymodal interaction near the wave bifurcation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 6, pp. 15-24. DOI: 10.18500/0869-6632-2012-20-6-15-24

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Spatial-temporal patterns in a multidimensional active medium formed due to polymodal interaction near the wave bifurcation

Borina Marija Yurevna, P.N. Lebedev Physical Institute of the Russian Academy of Sciences
Polezhaev Andrej Aleksandrovich, P.N. Lebedev Physical Institute of the Russian Academy of Sciences

Investigation of a set of amplitude equations, describing interaction of several modes which became unstable due to the wave bifurcation, is carried out. It is shown that as a result of competition between modes depending on the value of the parameter defining the strength of interaction only two regimes are possible: either quasi one-dimensional travelling waves (there exists only one nonzero mode) or standing waves (al the modes are nonzero). This result is supported by numerical experiments for the Gierer-Mainhrdt model modified by addition of one more equation for the second fast diffusing inhibitor.

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