Traveling waves for a model of individual clustering with logistic growth rate
H. Ibrahim, E. Nasreddine
Source abstract
We consider a traveling wave problem for a one-dimensional model of individual clustering or aggregation. This model, originally formulated by Grindrod [J. Math. Biol. 26(6), 651–660 (1988)], describes the mechanism of individual dispersion when individuals are able to utilize information about their local environment. Specifically, it assumes that each individual disperses randomly with probability δ and disperses deterministically so as to improve his reproductive rate with probability 1−δ. In this paper, we prove the existence of a traveling wave solution when the probability of random dispersion exceeds a critical value δ* uniquely determined by the biased individual velocity.
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