FILIPPOV TYPE PREY–PREDATOR SYSTEM FOR SELECTIVE HARVESTING OF PREY
-
Published:2024-01-10
Issue:
Volume:
Page:
-
ISSN:0218-3390
-
Container-title:Journal of Biological Systems
-
language:en
-
Short-container-title:J. Biol. Syst.
Author:
YADAV UGANTA1ORCID,
NAYAK A. K.1ORCID,
GAKKHAR SUNITA1ORCID
Affiliation:
1. Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India
Abstract
In this paper, the dynamics of a Filippov system with logistically growing prey and Holling Type II predation is explored. The selective nonlinear harvesting of prey is carried out when the ratio of prey to predator is above a specified threshold value. In order to prevent the extinction of both the species and sustainable economic gains, no harvesting is allowed when the ratio is below a threshold value. The equilibrium states and their stability for the individual smooth are analyzed. Filippov convex method is applied to determine the dynamics on the boundary. The sliding mode dynamics is scrutinized, and it is observed that there is no escaping region. The existence of boundary points, tangent points and pseudo-equilibrium points are established. The conditions are obtained for the visibility of the tangent points. The complex behavior within the sliding region is studied by experimenting with different initial conditions. The increase in harvesting effort may lead to extinction of both the species through the sliding region of the boundary. The change in the stability behavior of both the interior equilibrium states is investigated with respect to model parameters. Border cross bifurcates with threshold value as the bifurcation parameter is shown for both the interior equilibrium states.
Funder
Ministry of Human Resource Development
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology,Applied Mathematics,Agricultural and Biological Sciences (miscellaneous),Ecology