A Lotka–Volterra-Type Model Analyzed Through Different Techniques

Abstract

We consider a modified Lotka–Volterra model applied to the predator-prey system that can also be applied to other areas, for instance, the bank system. We show that the model is well-posed (nonnegativity of solutions and conservation law) and study the local stability using different methods. Firstly, we consider the continuous model, after which the numerical schemes of Euler and Mickens are investigated. Finally, the model is described using Caputo fractional derivatives. For the fractional model, besides well-posedness and local stability, we prove the existence and uniqueness of solution. Throughout the work, we compare the results graphically and present our conclusions. To represent graphically the solutions of the fractional model, we use the modified trapezoidal method that involves the modified Euler method.