Role of fear in predator–prey system with intraspecific competition

Predator–prey interaction is considered as a natural phenomenon in ecological system. An obvious question arises in ecosystem is that how predator affect the density of prey population. In most of the ecological models, predators reduce prey densities by direct killing which is a minor part in population dynamics. Experimental studies on vertebrate has shown that fear of predators can influence the behavioural pattern of prey population and reduce their reproduction. Mathematical models of predator–prey system with variety of predator functional responses with fear effect are studied recently. These studies ignore the fear effect on the death rate of prey species. Based on the above observation, we propose a mathematical model of predator–prey system with the cost of fear that affect reproduction and death rate of prey population. We also include a term modelling intraspecific competition within the predator population. This additional term limits the predator population growth for large predator to prey density ratios. 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. Numerical experiments are performed to test the theoretical results obtained for this model.