Intraspecific competition of predator for prey with variable rates in protected areas

Abstract

In this present study, we systematically explore the periodicity (almost periodic nature) of a dynamical system in time-varying environment, which portrays a special case of prey–predator model governed by non-autonomous differential equations. In particular, we investigate the dynamical characteristics of the underlying prey–predator model by considering modified Leslie–Gower-type model with Crowley–Martin functional response with time-dependent periodic variation of model parameters in a prey reserve area. We show the existence of globally stable periodic solutions. This perpetual prey oscillation results in persistent interference among predator, causing reduced feeding rate at high prey density. A comparative study between the two methods used to prove the existence of periodic (almost periodic) solution of the considered non-autonomous system is also discussed. After showing permanence, existence, uniqueness and global attractivity of the periodic (almost periodic) solution analytically, we demonstrate the typical prey and predator dynamics in time-varying environment using several numerical examples. Partial rank correlation coefficient technique is performed to address how the model output is affected by changes in a specific parameter disregarding the uncertainty over the rest of the parameters.