منابع مشابه
Bifurcation Pattern in Reaction-Diffusion Dissipative Systems
für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...
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Bifurcations of spatially nonhomogeneous periodic orbits and steady state solutions are rigorously proved for a reaction–diffusion system modeling Schnakenberg chemical reaction. The existence of these patterned solutions shows the richness of the spatiotemporal dynamics such as oscillatory behavior and spatial patterns.
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For a large class of reaction-diiusion systems on the plane, we show rigorously that m-armed spiral waves bifurcate from a homogeneous equilibrium when the latter undergoes a Hopf bifurcation. In particular, we construct a nite-dimensional manifold which contains the set of small rotating waves close to the homogeneous equilibrium. Examining the ow on this center-manifold in a very general exam...
متن کاملA stochastic pitchfork bifurcation in a reaction-diffusion equation
First we prove, for m 65, a lower bound on the dimension of the random attractor, which is of the same order in as the upper bound we derived in an earlier paper, and is the same as that obtained in the deterministic case. Then we show, for m = 1, that as passes through ¶ 1 (the rst eigenvalue of the negative Laplacian) from below, the system undergoes a stochastic bifurcation of pitchfor...
متن کاملGlobal Bifurcation for a Reaction-diffusion System with Inclusions
We consider a reaction-diffusion system exhibiting diffusion driven instability if supplemented by Dirichlet-Neumann boundary conditions. We impose unilateral conditions given by inclusions on this system and prove that global bifurcation of spatially nonhomogeneous stationary solutions occurs in the domain of parameters where bifurcation is excluded for the original mixed boundary value proble...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1984
ISSN: 0377-0427
DOI: 10.1016/0377-0427(84)90029-3