INSTABILITY OF TRAVELING-WAVE SOLUTIONS OF A POPULATION-MODEL WITH NONLOCAL EFFECTS

The authors study a single-species population model in the form of a s calar reaction-diffusion equation incorporating a time delay which, be cause of the assumption that the animals are moving, leads to an integ ral term in both space and time. In a previous paper, it was shown tha t small-amplitude periodic travelling wave solutions of the equation a rise via bifurcation from a uniform steady state. In this paper, it is shown, using a multiscale perturbation expansion, that these solution s are unstable. Numerical evidence suggesting in certain cases the exi stence of large-amplitude steady solutions is also presented.