Coexistence of three predators competing for a single biotic resource

International audienceWe construct a model of competition of three consumers for one single biotic resource ; simulations show that the three species coexist. Using singular perturbations theory we sketch a mathematical proof for this coexistence. The main mathematical tool used is an extension of the Pontryagin-Rodygin theorem on the ''slow'' motion of a ''slow-fast'' differential system when the ''fast'' motion possesses a stable limit cycle. The mathematical analysis is done within the framework of Non Standard Analysis