SPATIAL-TEMPORAL PATTERNS IN A MULTIDIMENSIONAL ACTIVE MEDIUM FORMED DUE TO POLYMODAL INTERACTION NEAR THE WAVE BIFURCATION
Cite this article as:
Борина М. Ю., Полежаев А. А. 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: https://doi.org/10.18500/0869-6632-2012-20-6-15-24
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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BibTeX
author = {М. Yu. Borina and Andrey Aleksandrovich Polezhaev},
title = {SPATIAL-TEMPORAL PATTERNS IN A MULTIDIMENSIONAL ACTIVE MEDIUM FORMED DUE TO POLYMODAL INTERACTION NEAR THE WAVE BIFURCATION},
year = {2012},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {20},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/spatial-temporal-patterns-in-multidimensional-active-medium-formed-due-to-polymodal},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2012-20-6-15-24},pages = {15--24},issn = {0869-6632},
keywords = {Active medium,diffusion instability,wave bifurcation,amplitude equations},
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. }}