Periodicity and limit cycle perturbation analysis of a predator–prey model with interspecific species’ interference, predator additional food and dispersal

We formulate a robust mathematical model for two predators having an overlapping dietary niche breadth. We use the Beddington–DeAngelis functional and numerical responses which are relevant in addressing the principle of competitive exclusion as species interact. The stabilizing effect of additional food in relation to the relative diffusivity D, and wave number k, has been investigated. Stability, dissipativity, permanance, persistence and periodicity of the model have been studied using the routine and limit cycle perturbation methods. Besides revealing irregular periodic travelling wave behaviour due to predator interference, numerical results also show oscillatory temporal dynamics resulting from additional food supplements combined with high predation rates.