Destabilizing effect of cannibalism on a structured predator-prey system |
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Authors: | Magnússon K G |
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Affiliation: | Division of Applied Mathematics and Computer Science, University of Iceland, Reykjavík, Iceland. kgm@rhi.hi.is |
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Abstract: | The dynamics of a predator-prey system, where the predator has two stages, a juvenile stage and a mature stage, are modelled by a system of three ordinary differential equations. The mature predators prey on the juvenile predators in addition to the prey. If the mortality rate of juveniles is low and/or the recruitment rate to the mature population is high, then there is a stable equilibrium with all three population sizes positive. On the other hand, if the mortality rate of juveniles is high and/or the recruitment rate to the mature population is low, then the equilibrium will be stable for low levels of cannibalism, but a loss of stability by a Hopf bifurcation will take place as the level of cannibalism increases. Numerical studies indicate that a stable limit cycle appears. Cannibalism can therefore be a destabilizing force in a predator-prey system. |
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