Switching effect on a two prey–one predator system with strong Allee effect incorporating prey refuge

In an environment, the food chains are balanced by the prey–predator interactions. When a predator species is provided with more than one prey population, it avails the option of prey switching between prey species according to their availability. So, prey switching of predators mainly helps to increase the overall growth rate of a predator species. In this work, we have proposed a two prey–one predator system where the predator population adopts switching behavior between two prey species at the time of consumption. Both the prey population exhibit a strong Allee effect and the predator population is considered to be a generalist one. The proposed system is biologically well-defined as the system variables are positive and do not increase abruptly with time. The local stability analysis reveals that all the predator-free equilibria are saddle points whereas the prey-free equilibrium is always stable. The intrinsic growth rates of prey, the strong Allee parameters, and the prey refuge parameters are chosen to be the controlling parameters here. The numerical simulation reveals that in absence of one prey, the other prey refuge parameter can change the system dynamics by forming a stable or unstable limit cycle. Moreover, a situation of bi-stability, tri-stability, or even multi-stability of equilibrium points occurs in this system. As in presence of the switching effect, the predator chooses prey according to their abundance, so, increasing refuge in one prey population decreases the count of the second prey population. It is also observed that the count of predator population reaches a comparatively higher value even if they get one prey population at its fullest quantity and only a portion of other prey species. So, in the scarcity of one prey species, switching to the other prey is beneficial for the growth of the predator population.