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

TL;DR

This paper critiques a previous claim about the stability of a predator-prey model with a square root functional response, providing detailed proof and numerical simulations that reveal complex phase behaviors.

Contribution

It clarifies the stability conditions of a modified Lotka-Volterra model with a square root response, challenging prior assumptions and highlighting the non-differentiability issue.

Findings

Global stability depends on parameters, contrary to previous claims

Phase portraits exhibit two distinct modes of behavior

Some initial conditions lead to finite-time convergence to the predator axis

Abstract

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.