Spatially-Structured Three-Species Models for Benthic Predation

In a recent study [1], an ordinary differential equation model has been given for one-prey (mussel) and one-predator (sea star) of a benthic community , representing their spatially-structured dynamics. We generalize this model in this paper and extend its scope to the dynamics of three species (one-prey, two-predators) of benthic community namely: mussel, sea star and spiny lobster. We present two models in this paper, one with the assumption that the prey reaches certain size and becomes resistant to both predators and the other when the large size prey becomes resistant to one predator but remains vulnerable to the other. It is seen that these models have the possibility of multiple equilibrium solutions whose existence and stability may be related to the crucial parameters of the two predators .