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Chaos and pattern formation in a spatial tritrophic food chain

We study the effects of local predation in a spatial version of the tritrophic food chain model introduced by Hastings and Powell. We show that the introduction of local predator-prey interactions have different implications on the dynamics of the predators and the preys. The time evolution equations for the spatially distributed predators involve averages over the local density of preys, whereas the equations for the preys involve double averages that depend on the local density of both preys and predators. The introduction of local predation also leads to spontaneous pattern formation and to qualitative changes in the global dynamics of the system. In particular, depending on the size of the predation neighborhoods, the chaotic strange attractor present in the original model of Hastings and Powell can be replaced by a stable fixed point or by an attractor with simpler topology.

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