Stability Analysis of Prey-Predator Model Migration with Holling Type-III Response Function in The Presence of Competition and Toxicity

Hasanuddin University, Mathematics Department, 90245, Tamalanrea, Makassar, Indonesia

^* Corresponding author: syamsuddint@gmail.com

Abstract

In this paper, we propose and investigate a prey-predator model with two zones contaminated with heavy metal toxicity, especially copper (Cu), which enter the reservation zone and the unreserved zone in the aquatic environment. The dynamics of the prey population in the ecosystem can migrate from the reservation zone to the unreserved zone or vice versa, while predators are assumed to look for prey in the unreserved zone. The dynamic behavior of the population is expressed as a system of differential equations based on food intake capacity and other factors. We introduce a predator population with a Holling type III predation response function, coupled with inter-specific competition among prey due to overlapping diets and assuming the prey is contaminated with copper metal toxicity. The presence of a positive equilibrium point, namely the interior equilibrium point, is analyzed and investigated for its stability using the Routh-Hurwitz stability test. Numerical simulations are carried out to verify the results of the analysis and dynamics of the system solution. The results of the analysis of the interior equilibrium point T₃ in each case is a stable point. This indicates a change in the balance of prey populations and predator populations.