Chaotic Dynamics of a Tri-Topic Food Chain Model with Beddington-DeAngelis Functional Response in Presence of Fear Effect

Abstract

The most important fact in the field of theoretical ecology and evolutionary biology is the strategy of predation for predators and the avoidance of prey from predator attack. A lot of experimental works suggest that the reduction of prey depends on both direct predation and fear of predation. We explore the impact of fear effect and mutual interference into a three-species food chain model. In this manuscript, we have considered a tri-topic food web model with Beddington-DeAngelis functional response between interacting species, incorporating the reduction of prey and intermediate predator growth because of the fear of intermediate and top predator respectively. We have provided parametric conditions on the existence of biologically feasible equilibria as well as their local and global stability also. We have established conditions of transcritical, saddle-node and Hopf bifurcation in vicinity of different equilibria. Finally, we performed some numerical investigations to justify analytical findings.Mathematics Subject Classification : 39A30, 92D25, 92D50.

An autonomous and nonautonomous predator–prey model with fear, refuge, and nonlinear harvesting: Backward, Bogdanov–Takens, transcritical bifurcations, and optimal control

“…They found that fear could stabilize a predator-prey system by excluding population oscillations. Recently, Roy and Alam [7], Sk et al [8,9], Mondal et al [10], and others [11,12] have studied their model incorporating fear effect.…”