A Comparative Study of Backward Euler and Adams-Moulton Methods for Lotka-Volterra Prey-Predator Model

Abstract

This research investigates the comparison between the backward Euler and Adams-Moulton methods in solving the Lotka-Volterra prey predator model, specifically analyzing the interaction between wolf and moose populations. The study aims to identify which numerical method provides a more accurate approximation of the model’s solutions. Data collected from the interactions between wolves and moose on Isle Royale from 1959 to 2019 was used, determining a carrying capacity of 21.24 for wolves and 948.15 for moose. When the initial population is below this carrying capacity, it tends to grow due to the availability of adequate resources. The comparison results revealed that the Adams-Moulton method provided the most accurate approximation, successfully achieving the primary objective of the research. The equilibrium and stability of the system were assessed by defining its dynamics through mathematical equations and evaluating the eigenvalues of the Jacobian matrix, resulting in a growth rate value of 0.5017. The system was found to be stable when the populations of moose and wolves oscillated with consistent amplitude, influenced by the growth rate. The findings emphasize the importance of carrying capacity and initial conditions in understanding equilibrium and stability in prey-predator interactions, contributing to population dynamics. This research aids in the development of effective conservation and management strategies for maintaining ecosystem balance.