Instability of travelling wave solutions of a population model with nonlocal effects

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Abstract
The authors study a single-species population model in the form of a scalar reaction-diffusion equation incorporating a time delay which, because of the assumption that the animals are moving, leads to an integral term in both space and time. In a previous paper, it was shown that small-amplitude periodic travelling wave solutions of the equation arise via bifurcation from a uniform steady state. In this paper, it is shown, using a multiscale perturbation expansion, that these solutions are unstable. Numerical evidence suggesting in certain cases the existence of large-amplitude steady solutions is also presented.

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