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ISSN 2542-1905 (Online)

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Borina M. J., 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:


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


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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