The influence of dispersal on a predator–prey system with two habitats

P. Gramlich, S.J. Plitzko, L. Rudolf, B. Drossel, and T. Gross
Journal of Theoretical Biology 398, 150-161, 2016.

Dispersal between different habitats influences the dynamics
and stability of populations considerably. Furthermore, these effects
depend on the local interactions of a population with other species.
Here, we perform a general and comprehensive study of the simplest
possible system that includes dispersal and local interactions, namely
a 2-patch 2-species system. We evaluate the impact of dispersal on
stability and on the occurrence of bifurcations, including pattern
forming bifurcations that lead to spatial heterogeneity, in 19 different
classes of models with the help of the generalized modelling approach.
We find that dispersal often destabilizes equilibria, but it can
stabilize them if it increases population losses. If dispersal is
nonrandom, i.e. if emigration or immigration rates depend on population
densities, the correlation of stability with dispersal rates is positive
in part of the models. We also find that many systems show all four
types of bifurcations and that antisynchronous oscillations occur
mostly with nonrandom dispersal.

(fulltext link)
doi: 10.1016/j.jtbi.2016.03.015
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