Uncertain parameter based dynamical model among the interaction of immature prey, mature prey and predator

Abstract

ABSTRACT In this paper, a mathematical model for the interaction of immature prey, mature prey, and predators has been developed. Here, most of the model parameters are considered fuzzy numbers. It is considered that the growth of immature prey depends on mature prey as well as the fear of predators. It is also considered that after remaining in the immature stage for a while, some immature prey transforms into mature prey. It is assumed that predators consume immature prey as well as mature prey. The intra-species competition among the mature prey has been considered. The boundedness of the solution of the proposed model is studied. Different equilibrium points have been determined, and the stability of the system has been investigated. The global stability of the system around the interior equilibrium point has been discussed through a geometric approach. From the analysis of the model, it is found that uncertain values of the model parameters have greatly impacted the solution of the model. It is observed that the increasing rate of transfer of immature prey to mature prey may destabilize the system. It is found that the system may become stable due to the increase in intra-species competition among mature prey.