Diffusion-driven period-doubling bifurcations.

@article{Kot1989DiffusiondrivenPB,
  title={Diffusion-driven period-doubling bifurcations.},
  author={Martin Kot},
  journal={Bio Systems},
  year={1989},
  volume={22 4},
  pages={279-87}
}
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. 

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