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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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
519.8
DOI: 
10.18500/0869-6632-2012-20-6-15-24

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

Autors: 
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
Abstract: 

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.

Key words: 
Active medium
diffusion instability
wave bifurcation
amplitude equations
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Received: 
15.02.2012
Accepted: 
11.05.2012
Published: 
29.03.2013
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