Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion

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7 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)449-467
Numero di pagine19
RivistaDefault journal
Volume65
Stato di pubblicazionePublished - 2016

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Turing Patterns
Cross-diffusion
Reaction-diffusion Model
Bifurcation
Multiple Scales
Pattern Formation
Stationary Solutions
Reaction-diffusion System
Chemical Reaction
System Modeling
Diffusion Coefficient
Chemical reactions
Term
Influence

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cita questo

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title = "Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion",
abstract = "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.",
author = "Lombardo, {Maria Carmela} and Gaetana Gambino and Sammartino, {Marco Maria Luigi} and Salvatore Lupo",
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T1 - Super-critical and sub-critical bifurcations in a reaction-diffusion Schnakenberg model with linear cross-diffusion

AU - Lombardo, Maria Carmela

AU - Gambino, Gaetana

AU - Sammartino, Marco Maria Luigi

AU - Lupo, Salvatore

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/198369

M3 - Article

VL - 65

SP - 449

EP - 467

JO - Default journal

JF - Default journal

ER -