One-Prey Two-Predator Model with Prey Harvesting in a Food Chain Interaction

摘要

The interaction between prey, secondary predator, and primary predator as a mathematical model of the one-prey and two-predator system with constant harvesting in prey population will be introduced in this article. Their interaction might describe as a food pyramid, with the preys is in the lowest level of the pyramid, secondary predators in the middle, and primary predators in the top of the pyramid. Human intervention to controlling prey population is needed and will be analyzed how this will effect on the existence of secondary predator and primary predator population. Equilibrium points and their existence criteria will be analyzed to find a threshold that will guarantee the coexistence of this system. Some numerical simulation will be given to illustrate the analytical results. We find that as long as harvesting rate in prey population is smaller than prey intrinsic growth rate, coexistence might achieve.