Diffusion instability in a threevariable reaction–diffusion model

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Investigation of occurrence of diffusion instability in a set of three reaction–diffusion equations is carried out. In the general case the condition for both Turing and wave instabilities are obtained. Qualitative properties of the system, in which the bifurcation of each of the two types can take place, are clarified. In numerical experiments it is shown that if the corresponding conditions are met in the nonlinear model, spatiotemporal patterns are formed, which are predicted by linear analysis.

Keywords: diffusion instability, Turing instability, wave instability
Citation in English: Borina M.Y., Polezhaev A.A. Diffusion instability in a threevariable reaction–diffusion model // Computer Research and Modeling, 2011, vol. 3, no. 2, pp. 135-146
Citation in English: Borina M.Y., Polezhaev A.A. Diffusion instability in a threevariable reaction–diffusion model // Computer Research and Modeling, 2011, vol. 3, no. 2, pp. 135-146
DOI: 10.20537/2076-7633-2011-3-2-135-146
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
  • Maria Yur’evna Borina, A. A. Polezhaev. On the mechanisms for formation of segmented waves in active media. // Computer Research and Modeling. 2013. — V. 5, no. 4. — P. 533. DOI: 10.20537/2076-7633-2013-5-4-533-542
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