On the mechanisms for formation of segmented waves in active media

Borina M.Y., Polezhaev A.A.
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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 microemulsion. 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
Citation in English: Borina M.Y., Polezhaev A.A. On the mechanisms for formation of segmented waves in active media // Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 533-542
Citation in English: Borina M.Y., Polezhaev A.A. On the mechanisms for formation of segmented waves in active media // Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 533-542
DOI: 10.20537/2076-7633-2013-5-4-533-542
URL: http://crm-en.ics.org.ru/journal/article/2063/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Maxim Borisovich Kuznetsov. Investigation of Turing structures formation under the influence of wave instability. // Computer Research and Modeling. — 2019. — V. 11, no. 3. — P. 397. DOI: 10.20537/2076-7633-2019-11-3-397-412
  • Maxim Borisovich Kuznetsov, A. A. Polezhaev. The mechanism of formation of oscillons - localized oscillatory structures. // Computer Research and Modeling. — 2015. — V. 7, no. 6. — P. 1177. DOI: 10.20537/2076-7633-2015-7-6-1177-1184
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