Abstract
We consider Turing-type reaction-diffusion equations and study (via computer simulations) how the relationship between initial conditions and the asymptotic steady state solutions varies as a function of the boundary conditions. The results indicate that boundary conditions which are non-homogeneous with respect to the kinetic steady state give rise to spatial patterns which are much less sensitive to variations in the initial conditions than those obtained with homogeneous boundary conditions, such as zero flux conditions. We also compare linear pattern predictions with the numerical solutions of the full nonlinear problem.
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This work supported in part by U.S. Army Grant DAJA 37-81-C-0220 and the Science and Engineering Research Council of Great Britain Grant GR/c/63595
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Arcuri, P., Murray, J.D. Pattern sensitivity to boundary and initial conditions in reaction-diffusion models. J. Math. Biology 24, 141–165 (1986). https://doi.org/10.1007/BF00275996
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DOI: https://doi.org/10.1007/BF00275996