Presented is a reaction-diffusion model for the interaction of pioneer and climax species. For certain parameters the system exhibits bistability and traveling wave solutions. Specifically, we show that when the climax species diffuses at a slow rate there are traveling wave solutions which correspond to extinction waves of either the pioneer or climax species. A leading order analysis is used ...

Periodic traveling waves (wavetrains) have been extensively studied for reaction-diffusion equations. One important motivation for this work has been the identification of periodic traveling wave patterns in spatiotemporal data sets in ecology. However, for many ecological populations, diffusion is no more than a rough phenomenological representation of dispersal, and spatial convolution with a...

We consider traveling wave solutions to spatially discrete reaction-diiusion equations with nonlocal variable diiusion and bistable nonlinearities. For the case of spatially periodic diiusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly deened in the general periodic case and we provide an explici...