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Stability Analysis of Prey-Predator Model Migration in Mangrove Ecosystems with Holling Type-III Response Function
Agus S.
Aip Conference Proceedings
Abstract
This paper discusses the dynamics and interaction of prey and predator populations in an ecosystem consisting of two zones, namely the reservation zone and the unreserved zone. The prey population in the ecosystem can migrate from the reservation zone to the unreserved zone and vice versa, while the predator population is assumed to be looking for prey in the unreserved zone. The dynamics of predator and prey are expressed in the form of a system of differential equations based on food intake capacity and some other factors. In the interaction mechanism between the prey and the predator, the Holling type III predation response function is considered. The existence of an interior equilibrium point of the model is analyzed and investigated for its stability using the linearization method and the Routh-Hurwitz stability test. There is a certain condition where, with the appropriate parameter values, the interior equilibrium point exists and is stable. When the migration rate from the unreserved zone is gradually increased within a certain range of values, the equilibrium point also changes but remains stable. The prey and predator populations in an unreserved zone decrease while the prey population in the reservation zone increases. Numerical simulations are carried out to verify the analytical results and the behavior of the populations.