Complex dynamics of two prey–one predator model together with fear effect and harvesting efforts in preys

In this paper, a two prey–one predator model with different types of growth rate and mixed functional responses is proposed and analysed. Moreover, we considered anti-predation behaviour and constant harvesting effort in both the prey populations. The positivity and boundedness of the system are studied. The criteria for the extinction of the predator–prey populations are discussed. Analytically, we have studied the criteria for existence and stability of different equilibrium points. In addition, we have derived sufficient conditions for local bifurcations such as transcritical and Hopf bifurcation. We discussed that the effect of fear not only reduces prey populations, but also decreases the rate of growth of the predator population. Computer simulations are performed to validate our analytical results. The biological implications of analytical and numerical results are critically discussed.