DYNAMICAL BEHAVIOR IN THE COMPETITIVE MODEL INCORPORATING THE FEAR EFFECT OF PREY DUE TO ALLELOPATHY WITH SHARED BIOTIC RESOURCES

This research develops a mathematical model of a natural phenomenon, namely sea snails that can release toxins (allelopathy) so that non-toxic sea snails become afraid. In addition, toxic and non-toxic sea snails share biotic resources. Based on the existing phenomenon, the model of fear effect caused by allelopathy in the competitive interaction model with shared biotic resources will be studied. In this system, three equilibrium points are obtained: extinction point of prey, extinction point of predator, and coexisting point under certain conditions. Analysis of local stability at equilibrium points by linearization shows that all equilibrium points are asymptotically stable with certain conditions. Numerical simulations at the equilibrium point show the same results as the analysis results. Then, numerical continuity was carried out by selecting variation of the fear effect parameter for Numerical continuity results show that changes in these parameters affect the population of toxic and non-toxic species, marked by the emergence of Transcritical bifurcations, Bifurcation occurs at the first Saddle-Node bifurcation at and the second Saddle-Node bifurcation at