Anaysis of Predator-Prey Dynamics Using Holling Type I & II Response Functions with Kleptoparasitism and Anti-Predator Behavior - Tassha Putri; Dian Savitri (Department of Mathematics, Universitas Negeri Gorontalo, 2026)
Predator-prey interactions involving 3 species in an African forest ecosystem between Deer, Hyena and Lion considering the influence of kleptoparasitism and anti-predator behaviour using Holling type I & II functional responses. This predator prey model is constructed based on the assumption that the behaviour of the second predator Hyena often has the ability to defend itself against other predators such as fleeing, fighting, and intimidating which is called anti-predator behaviour. Based on the existing phenonema, the objectives of this study are to determine the model construction, equilibrium point analysis and stability, as well as numerical simulation and interpretation of the prey-prey model using Holling type I & II functional responses in the presence of kleptoparasitism and anti-predator behaviour. The calculation analysis in this study was carried out by finding the equilibrium point and stability analysis. The results of the dynamic analysis show that there are five equilibrium points with the type of stability, namely E_1(x, y, z) = (0, 0, 0) which states the extinction of the three populations, point equilibrium E_2(x, y, z) = (K, 0, 0) which represents the extinction of the first predator and second predator populations, point equilibrium E_3(x, y, z) = (-θ_2θ_2b-μ_2,0,-rμ_2(K(βθ_2-μ_2)+θ_2)Kβ_2(bθ_2-μ)^2) which expresses extinction in the first predator population, point equilibrium E_4(x,y,z) = (θ_1μ_1,r(μ_1K-θ_1)μ_1Kβ_1,0) which expresses extinction at the second predator, and equilibrium point E_5(x^*,y^*,z^*) which states that all three populations can coexist. Numerical simulation results show the existence of double stability at points E_4 and E_6 when the parameter values μ_1 = 0.3, μ_2 = 0.12 and double stability occurs again at points E_4 and E_3 when the parameter variation values μ_1 = 0.3, μ_2 = 0.158.