Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model

This paper deals with dynamical analysis of an ecological model. This model includes two logistically growing prey species, namely, Prey X and Prey Y , and the third species Z behaves as the predator, predating both Prey X and Prey Y according to the extended Holling type‐II functional response. Furthermore, the effect of fear is incorporated in the growth rate of both species Prey X and Prey Y due to the predator Z . All the biologically possible steady state points are explored, and their local stability as well as global stability is analyzed based on the sample parameters. Next, we investigate the occurrence of local bifurcations around each steady state points by taking the value of the birth rate, death rate, and fear parameter as a bifurcation parameter. Finally, we perform extensive numerical simulations to support the evidence of our analytical results.