Nonhomogeneous spatial distributions of populations |
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Authors: | K P Hadeler U an der Heiden and F Rothe |
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Institution: | (1) Lehrstuhl für Biomathematik, Universit?t Tübingen, Auf der Morgenstelle 28, D-7400 Tübingen, Federal Republic of Germany;(2) Tübingen |
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Abstract: | Summary Spatial inhomogeneities such as nonconstant population densities usually will be attributed to random effects or to an inhomogeneous
substrate. Such an explanation may be incorrect since from certain chemical reactions it is known that the interaction of
species together with diffusion may generate nonhomogeneous spatial structures. However, the effect of boundary conditions
has been so far neglected. In this paper nonlinear and linear interaction-diffusion models are investigated under various
side-conditions by analytic methods and by computer simulations. A remarkable fact, as compared with earlier results in the
field, is the example of an interaction-diffusion process which in the whole space has only the constant as a stable limit
distribution, whereas the introduction of a side condition, e.g. a population reservoir or a barrier, leads to standing spatial
population waves. |
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