Study of fear mechanism in predator-prey system in the presence of competitor for the prey

Abstract

Predator-prey relationships are one of the most commonly observed phenomena in ecosystem. In most of the ecological models, predators reduce prey densities by direct killing. A field study on vertebrate has shown that fear of predators can influence the behavioural pattern of prey population and reduce their reproduction. Most of the recent studies usually consider simplified systems in which predators only attack a single prey species. These studies ignore the impact of diversity of non-prey species. Based on the above observation, we propose a mathematical model of predator-prey system with cost of fear where prey population has a competitor (non-prey). Basic results on the positivity and boundedness of the solutions, feasibility of equilibria, local and global stability and uniform persistence (ensuring the long term survival of the species) and limit cycles and its nature are investigated. We also investigate the impact of fear effect on the model. We observe that increase amount of fear reduce the predator density at the coexistence equilibrium point. Numerical experiments are performed to test the theoretical results obtained for this model.