Chaos and pattern formation in a spatial tritrophic food chain

摘要: Abstract The model of Hastings and Powell describes a tritrophic food chain that exhibits chaotic dynamics. assumes the populations are homogeneously mixed, so probability any two individuals interact is uniform space can be ignored. In this paper we propose spatial version in which predators seek their preys only finite neighborhood home location, breaking mixing hypothesis. Treating both time as discrete variables derive set coupled equations describe evolution at each site domain. We show introduction local predator–prey interactions result qualitatively distinct dynamics predator prey populations. for involve averages over density preys, whereas double averages, where appear. Our numerical simulations predation also leads to spontaneous pattern formation qualitative changes global system. particular, depending on size neighborhoods, strange attractor present original replaced by stable fixed point or an simpler topology.