Search

Recent field experiments have shown that predators influence the prey population not only by direct consumption but also by stimulating various defensive strategies. The cost of these defensive strategies can include energetic investment in defensive structures, reduced energy income, lower mating success, and emigration which ultimately reduces the reproduction of prey. To explore the effect of these defensive strategies (anti‐predator behaviors), a modified Leslie–Gower predator–prey model with the cost of fear has been considered. Gestation delay is also incorporated in the system for a more realistic formulation. Boundedness, equilibria and stability analysis are performed for the temporal system. By considering gestation delay as a bifurcation parameter, the existence of Hopf‐bifurcation around the interior equilibrium point is discussed together with the direction, stability, and period of bifurcating solutions arising through Hopf‐bifurcation. The spatial extension of the proposed model incorporating density‐dependent cross‐diffusion is also investigated and the conditions for diffusion‐driven instability are obtained. To illustrate the analytical findings, detailed numerical simulations are performed. Biologically realistic Turing patterns such as spots, spots and stripes mixture, and labyrinthine type patterns are identified. It is found that the fear level has a stabilizing impact on delay induced destabilization and both stabilizing and destabilizing effects on Turing instability. [ABSTRACT FROM AUTHOR]

Recent demographic experiments have demonstrated that both birth and survival in free-living animals are essentially affected due to having sufficient exposure to predators and further leaving physiological stress effects. In this paper, we have proposed and analyzed a predator–prey interaction model with Beddington–DeAngelis functional response (BDFR) and incorporating the cost of fear into prey reproduction. Stability analysis and the existence of transcritical bifurcation are studied. For the spatial system, the Hopf-bifurcation around the interior equilibrium, stability of homogeneous steady state, direction and stability of spatially homogeneous periodic orbits have been established. Using Normal form of the steady state bifurcation, the possibility of pitchfork bifurcation has been established. The impact of the level of fear and mutual interference on the stability and Turing patterns of the spatiotemporal system have been discussed in detail. Simulation results ensure that the fear of predator stabilizes the system dynamics and cost the overall population size of the species. [ABSTRACT FROM AUTHOR]