Examination of stability of the mathematical predator-prey model by observing the distance between predator and prey

Maintaining distance is one of the strategies that can be applied by prey to defend themselves or to avoid predatory attacks. This defense behavior can affect predation rates. The distance or difference in the number of prey and predator populations will affect the level of balanced ecosystem. The distance is also affecting predation rate, when there’s a long distance between prey and predator thus the predation rate decreases and vice versa. The purpose of this thesis is to analyze the stability of the mathematical equilibrium on predator-prey model by observing the distance. There are two types of model being observed, type one uses exponential growth model and type two is using a logistic growth model. The analytics results obtain three equilibrium points, namely the unstable extinction equilibrium point, and the asymptotically stable predator extinction with certain conditions and asymptotically stable coexistence with certain conditions. Then numerical simulation is conducted to support the analytical results.