Coexistence of competing predators in a coral reef ecosystem

An analysis is made using a four-dimensional mathematical model where there is a constant rate of flow of input nutrient. An organism is introduced in the model which is growing by taking in that nutrient. Two other predators on that organism are also introduced. The predators at the second and third trophic levels belong to the same species, though of different age groups. The predator at the third trophic level exhibits a distinct cannibalistic attitude to the predator of the second trophic level. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the species associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained when one or more of the predators go extinct. Under appropriate circumstances a positive rest point of the system is obtained. Computer simulations have been carried out to illustrate different analytical results.