Comment on predator-prey dynamical behavior and stability with square root functional response

In this research, we revisit the paper by Pal et al. [Int. J. Appl. Comput. Math (2017) 3:1833-1845] and comment on the claim that global stability of the interior equilibrium point depends on some key parameters. This is not true, and we have provided detailed proof to this effect. The considered model is a modified Lotka-Volterra model where square root functional response is involved. The square root functional response is non-differentiable at the origin and hence cannot be studied with standard local stability tools. Furthermore, our numerical simulations indicate that we can classify the phase portrait into two modes of behavior where some positive initial conditions converge towards the predator axis in finite time

Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions

Dual fear phenomenon in an eco-epidemiological model with prey aggregation

This study presents a thorough analysis of an eco-epidemiological model that integrates infectious diseases in prey, prey aggregation, and the dual fear effect induced by predators. We establish criteria for determining the existence of equilibrium points, which carry substantial biological significance. We establish the conditions for the occurrence of Hopf, saddle-node, and transcritical bifurcations by employing fear parameters as key bifurcation parameters. Furthermore, through numerical simulations, we demonstrate the occurrence of multiple zero-Hopf (ZH) and saddle-node transcritical (SNTC) bifurcations around the endemic steady states by varying specific key parameters across the two-parametric plane. We demonstrate that the introduction of predator-induced fear, which hinders the growth rate of susceptible prey, can lead to the finite time extinction of an initially stable susceptible prey population. Finally, we discuss management strategies aimed at regulating disease transmission, focusing on fear-based interventions and selective predation via predator attack rate on infectious prey