Analysis of a Predator-Prey Model: A Deterministic and StochasticApproach

Abstract

This paper investigates the deterministic and stochastic fluctuations of a predator-prey model. The predator is experienced in hunting two different prey simultaneously. Each prey has logistic growth in the absence of the predator. The rate of experience of the predator in hunting each prey is varied using a simulated dataset. The deterministic and stochastic nature of the dynamics of the system are investigated. Stability analysis is performed, using slight perturbation around the non-zero, interior equilibrium point, to determine where the system loses stability. The variation of the predatory experience parameter causes the system to experience Hopf bifurcations. These stability changes and the addition of stochastic noise are explored using time series graphs. The co-existence and extinction of the populations are affected over time .