Dynamical analysis of a prey-predator model with specific mortality of predator under the influence of fear felt by prey

Abstract

Predator-prey interactions are a core component of theoretical ecology, crucial in establishing community structure and preserving ecological diversity. The effect of fear on prey by predator species and the maximal mortality rate of predator species is currently becoming an essential topic in ecology. The present work focuses on a prey-predator model that incorporates a specific mortality function for the predator species and a simplified Holling type IV functional response. Furthermore, the model incorporates an intraspecific competition among individuals of the prey species, the natural mortality rate of prey species, and the effect of fear on the prey population produced by predators in order to get more accurate and realistic dynamics. An analysis is conducted to determine the feasibility and stability conditions of equilibrium points in terms of the model parameters. The condition for the existence of at least one interior equilibrium point has been derived in terms of the model parameters. Several types of local bifurcations have been observed in the system such as transcritical bifurcation, saddle node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, Generalized Hopf bifurcation, Cusp bifurcation, ‘Saddle node bifurcation of limit cycle’ and a global bifurcation namely Homoclinic Bifurcation is also observed. Furthermore, the effect of hysteresis on our proposed model have been discussed. Numerical simulations have been performed using MATLAB and MATCONT to illustrate our analytical findings.