Diffusion-driven period-doubling bifurcations.

Discrete-time growth-dispersal models readily exhibit diffusive instability. In some instances, this diffusive instability parallels that found in continuous-time reaction-diffusion equations. However, if a sufficiently eruptive prey is held in check by a predator, predator overdispersal may also lead to one or a series of diffusion-driven period-doubling bifurcations. Quite common discrete-time predator-prey models exhibit this new brand of diffusive instability.