Summary
We study the effect of spatial diffusion on oscillatory states in arbitrary multi-species growth models having hereditary terms. We show that it is a general principle that the addition of spatial diffusion to a stable oscillatory ecological community induces a periodic diffusion wave in which the original wavenumber (or phase) evolves according to a nonlinear evolution equation of generalized Burgers' type.
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Supported in part by the U.S. Army Research Office (Durham) under Contract DAHC-04-68-C-0006 and by the National Science Foundation under Grant GP-32157X2
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Cohen, D.S., Rosenblat, S. Multi-species interactions with hereditary effects and spatial diffusion. J. Math. Biology 7, 231–241 (1979). https://doi.org/10.1007/BF00275726
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DOI: https://doi.org/10.1007/BF00275726