  A non-Markovian stochastic predator-prey model is introduced in which the
prey are immobile plants and predators are diffusing herbivors. The model is
studied by both mean-field approximation (MFA)and computer simulations. The MFA
results a series of bifurcations in the phase space of mean predator and prey
densities, leading to a chaotic phase. Because of emerging correlations between
the two species distributions, the interaction rate alters and if it is set the
value which is obtained from the simulation, then the chaotic phase disappears.
