Drivers of pattern formation in a predator-prey model with defense in fearful prey

Existence of predator is routinely used to induce fear and anxiety in prey which is well known for shaping entire ecosystem. Fear of predation restricts the development of prey and promotes inducible defense in prey communities for the survival. Motivated by this fact, we investigate the dynamics of a Leslie-Gower predator prey model with group defense in a fearful prey. We obtain conditions under which system possess unique global-in-time solutions and determine all the biological feasible states of the system. Local stability is analyzed by linearization technique and Lyapunov direct method has been applied for global stability analysis of steady states. We show the occurrence of Hopf bifurcation and its direction at the vicinity of coexisting equilibrium point for temporal model. We consider random movement in species and establish conditions for the stability of the system in the presence of diffusion. We derive conditions for existence of non-constant steady states and Turing instability at coexisting population state of diffusive system. Incorporating indirect prey taxis with the assumption that the predator moves toward the smell of prey rather than random movement gives rise to taxis-driven inhomogeneous Hopf bifurcation in predator-prey model. Numerical simulations are intended to demonstrate the role of biological as well as physical drivers on pattern formation that go beyond analytical conclusions.

Automated summary

Fear of predation in prey can restrict their development and promote defense mechanisms, shaping the entire ecosystem. The study investigates the dynamics of fearful prey with group defense, analyzing stability and potential bifurcations in the system. Consideration of diffusion and Hopf bifurcations are also important factors in determining system behavior.