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This article is cited in 2 scientific papers (total in 2 papers)
MATHEMATICAL MODELING AND NUMERICAL SIMULATION
On the mechanisms for formation of segmented waves in active media
M. Yu. Borina, A. A. Polezhaev P.N. Lebedev Physical Institute of the Russian Academy of Sciences
Russia, 119991, Moscow, Leninskiy prospekt, 53
Abstract:
We suggest three possible mechanisms for formation of segmented waves and spirals. These structures were observed in the Belousov–Zhabotinsky reaction dispersed in a water-in-oil aerosol OT micro-emulsion. The first mechanism is caused by interaction of two coupled subsystems, one of which is excitable, and the other one has Turing instability depending on the parameters. It is shown that, segmented spirals evolve from ordinary smooth spirals as a result of the transverse Turing instability. We demonstrate that depending on the properties of subsystems different segmented spirals emerge. For the second mechanism we suggest "splitting" of the traveling wave in the vicinity of the bifurcation point of codimension-2, where the boundaries of the Turing and wave instabilities intersect. Finally we show that the segmented waves can emerge in some simple two-component reaction-diffusion models having more than one steady state, particularly in a FitzHugh–Nagumo model.
Keywords:
segmented waves and spirals, excitable media, diffusion instability.
Received: 17.05.2013 Revised: 27.09.2013
Citation:
M. Yu. Borina, A. A. Polezhaev, “On the mechanisms for formation of segmented waves in active media”, Computer Research and Modeling, 5:4 (2013), 533–542
Linking options:
https://www.mathnet.ru/eng/crm415 https://www.mathnet.ru/eng/crm/v5/i4/p533
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Abstract page: | 110 | Full-text PDF : | 36 | References: | 23 |
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