Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion
| Autor: | S. Lupo, Marco Sammartino, Gaetana Gambino, Maria Carmela Lombardo |
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| Přispěvatelé: | Gambino, G., Lombardo, M., Lupo, S., Sammartino, M. |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Steady state Applied Mathematics General Mathematics Numerical analysis 010102 general mathematics Pattern formation Settore MAT/01 - Logica Matematica 01 natural sciences 010305 fluids & plasmas Nonlinear system Activator-inhibitor kinetics Cross-diffusion Turing instability Amplitude equations Amplitude 0103 physical sciences Reaction–diffusion system Statistical physics 0101 mathematics Constant (mathematics) Settore MAT/07 - Fisica Matematica Turing computer computer.programming_language |
| Zdroj: | Ricerche di Matematica. 65:449-467 |
| ISSN: | 1827-3491 0035-5038 |
| DOI: | 10.1007/s11587-016-0267-y |
| Popis: | In this paper the Turing pattern formation mechanism of a two components reaction-diffusion system modeling the Schnakenberg chemical reaction is considered. In Ref. (Madzavamuse et al., J Math Biol 70(4):709–743, 2015) it was shown how the presence of linear cross-diffusion terms favors the destabilization of the constant steady state. We perform the weakly nonlinear multiple scales analysis to derive the equations for the amplitude of the Turing patterns and to show how the cross-diffusion coefficients influence the occurrence of super-critical or sub-critical bifurcations. We present a numerical exploration of far from equilibrium regimes and prove the existence of multistable stationary solutions. |
| Databáze: | OpenAIRE |
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