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

被引：27

作者：

Gambino G. ^{[1
]}

Lombardo M.C. ^{[1
]}

Lupo S. ^{[1
]}

Sammartino M. ^{[1
]}

机构：

[1] Department of Mathematics and Computer Science, University of Palermo, Via Archirafi, 34, Palermo

来源：

Ricerche di Matematica | 2016年 / 65卷 / 2期

关键词：

Activator-inhibitor kinetics; Amplitude equations; Cross-diffusion; Turing instability;

D O I：

10.1007/s11587-016-0267-y

中图分类号：

学科分类号：

摘要：

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. © 2016, Università degli Studi di Napoli Federico II"."

引用

页码：449 / 467

页数：18

共 38 条

[1]

Aragon J., Barrio R., Woolley T., Baker R., Maini P., Nonlinear effects on Turing patterns: time oscillations and chaos, Phys. Rev. E, 86, 2, (2012)

[2]

Atis S., Saha S., Auradou H., Salin D., Talon L., Autocatalytic reaction fronts inside a porous medium of glass spheres, Phys. Rev. Lett, 110, 14, (2013)

[3]

Barbera E., Consolo G., Valenti G., Spread of infectious diseases in a hyperbolic reaction-diffusion susceptible-infected-removed model, Phys. Rev. E, 88, 5, (2013)

[4]

Barreira R., Elliott C.M., Madzvamuse A., The surface finite element method for pattern formation on evolving biological surfaces, J. Math. Biol, 63, 6, pp. 1095-1119, (2011)

[5]

Bilotta E., Pantano P., Emergent patterning phenomena in 2 D cellular automata, Artif. Life, 11, 3, pp. 339-362, (2005)

[6]

Bilotta E., Pantano P., Stranges F., A gallery of Chua attractors: Part II, International Journal of Bifurcation and Chaos, 17, 2, pp. 293-380, (2007)

[7]

Bozzini B., Gambino G., Lacitignola D., Lupo S., Sammartino M., Sgura I., Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth, Comput. Math. Appl, 70, pp. 1948-1969, (2015)

[8]

Cangelosi R., Wollkind D., Kealy-Dichone B., Chaiya I., Nonlinear stability analysis of Turing patterns for a mussel-algae model, J. Math. Biol, pp. 1-46, (2014)

[9]

Capone F., De Luca R., Rionero S., On the stability of non-autonomous perturbed Lotka-Volterra models, Appl. Math. Comput, 219, 12, pp. 6868-6881, (2013)

[10]

Chattopadhyay J., Tapaswi P., Effect of cross-diffusion on pattern formation—a nonlinear analysis, Acta Appl. Math, 48, pp. 1-12, (1997)

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