Comparison of The Trapezoidal and Adam Bashforth Approaches in The Lotka-Volterra Prey-Predator Dynamics

Abstract

This study primarily focuses on comparing the numerical methods of the Adams-Bashforth and Trapezoidal methods with the exact solution for solving the Lotka-Volterra prey-predator model. These methods are evaluated for their ability to reliably and accurately solve the non-linearity of the model. Based on the results, both methods offer precise solutions, with the Adams-Bashforth method providing a more accurate approximation for short-term predictions and the Trapezoidal method demonstrating better stability for long-term simulations. The study utilizes data from lynx-rabbit and bat-moth interactions to assess the performance of these methods using software tools. For both models, the short-term predictions align closely with observed data, while long-term stability analyses reveal the strengths of the Trapezoidal method. The equilibrium and stability analyses offer critical insights into the long-term behavior and stability of the system. The predator population trails behind the prey population: a rise in prey numbers is followed by a delayed increase in predator numbers as predators consume more prey. The phase portraits show the regularity of these oscillations. The curves move counterclockwise: prey numbers increase when predator numbers are at their lowest, and prey numbers decrease at their highest. These insights are essential for understanding and predicting the dynamics of predator-prey interactions and have significant implications for ecological modeling and conservation strategies.