1
King Khalid University, Faculty of Science, Department of Mathematics, Abha 9004, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
10.1016/j.joems.2014.06.020
Abstract
The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008). The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.
Aly, S. (2016). Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion. Journal of the Egyptian Mathematical Society, 24(1), 25-29. doi: 10.1016/j.joems.2014.06.020
MLA
Shaban Aly. "Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion", Journal of the Egyptian Mathematical Society, 24, 1, 2016, 25-29. doi: 10.1016/j.joems.2014.06.020
HARVARD
Aly, S. (2016). 'Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion', Journal of the Egyptian Mathematical Society, 24(1), pp. 25-29. doi: 10.1016/j.joems.2014.06.020
VANCOUVER
Aly, S. Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion. Journal of the Egyptian Mathematical Society, 2016; 24(1): 25-29. doi: 10.1016/j.joems.2014.06.020
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