| Abstrakt: |
This research is a literature study on predator-prey models with functional Holling II responses and cannibal predators and natural death of prey. The purpose of this study is to determine of the predator-prey model and to analyse the stability at each equilibrium point found. The novelty of this research is that it assumes a cannibalistic predator-prey model with a type II Holling response function, where the model will impact the stability of different predator prey populations. The predator prey model is an autonomous system with two differential equations. There are ten parameters obtained, namely K, r1, r2, a1, a2, b1, b2, c1, c2 and m. The model obtains four equilibrium points, namely E1(0,0) where the condition is that the predator and prey populations are extinct, E2(0, Y2) where the prey population is extinct, E3(X3, 0) where the predator population is extinct and E4(X5, Y5) where both populations exist. The four equilibrium points are local asymptotically stable with several conditions for E1(0,0) to be stable if r11 and r22, E2(0, Y2) to be asymptotically stable if r 1 − c 1 < a 1 b 2 (r 2 − c 2) a 2 − m (r 2 − c 2) and D* < 0, for E3(X3, 0) to be stable if K 2 < X 3 < b 1 (c 2 − r 2) m (r 2 − c 2) + a 1 , and E5 (X5, Y5) to be asymptotically stable under certain conditions. These results have been confirmed through numerical simulations using matlab. [ABSTRACT FROM AUTHOR] |
