6 Result(s)
within
Article
T. Erneux
English
Mathematical and Computational Biology
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Article
Stability of rotating chemical waves
We investigate the stability of rotating waves of reaction-diffusion equations by deriving the bifurcation equations for the simplest time-periodic patterns defined in the r, θ plane of polar coordinates. We prov...
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Article
Transition from polar to duplicate patterns
The existence of symmetric nonuniform solutions in nonlinear reaction-diffusion systems is examined. In the first part of the paper, we establish systematically the bifurcation diagram of small amplitude solut...
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Article
The bifurcation diagram of a model chemical reaction—II. Two dimensional time-periodic patterns
The bifurcation equations of a general reaction-diffusion system are derived for a circular surface. Particular attention is directed to the deformation of the circular boundary into an elliptic shape. This le...
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Article
Chemical patterns in circular morphogenetic fields
A model of morphogenetic pattern formation recently proposed by Frenchet al. (1976) is investigated in relation to the properties of reaction-diffusion systems operating on two-dimensional circular medium. One of...
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Article
Bifurcation diagram of a model chemical reaction—I. Stability changes of time-periodic solutions
The stability properties of the first two time-periodic solutions bifurcating from an unstable uniform steady-state are analyzed for a model chemical system subject to zero fluxes at the boundaries. The existe...
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Article
Turing's theory in morphogenesis
Bifurcation theoretical and numerical analyses of one of Turing's models are performed. It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus e...
