Impact of Fear Effect in a Two Prey-One Predator System with Switching Behaviour in Predation

We study a class of models in which generalist predator utilizes two distinct prey species as their food sources. Several field data and experiments exhibit that predator may switch it's predation behaviour depending upon the abundance of each prey population and also it is observed that fear for predator reduces the reproduction of prey populations. Based on these experimental evidences, we improve our two prey-one predator model by including the cost of fear into prey reproduction and switching mechanism in predation. Well-posedness of our model is verified by exploring the basic dynamical properties of the system. All the biologically feasible steady states and their stability conditions are derived in terms of model parameters. Our model system experiences transcritical bifurcation for fear parameters as bifurcation parameters. We identify the parameter regions associated with prey-1 free, prey-2 free, predator free and coexisting equilibria in various parametric planes. We further notice that high level of perceived fear of a prey species and the superior quality of that prey (as food source of predator) may increase the possibility of survival of that species and stability of coexistence of the system tended to be promoted. Switching behaviour suppresses the non-equilibrium dynamics and increases the chance of stabilization at coexistence steady state. We perform numerical simulations to verify our analytical findings and analyze the biological relevancy in nature.

Automated summary

Research shows that predators can change their predation behavior based on the abundance of prey populations, while fear of predators can reduce the reproduction of prey populations. By incorporating fear costs and predation switching mechanisms into the model, multiple steady states exist and fear parameters cause transcritical bifurcation in the system.