ABSTRACT
We consider a modified Lotka-Volterra model with a Michaelis-Menten type functional response with relevance to the bank system. We prove the model is well posed (non-negativity and boundedness of the solutions) and study the local stability using different methods. Firstly, we consider the continuous model. After, we investigate the dynamical consistency of two numerical schemes: Euler and Mickens. Finally, the model is described using Caputo fractional derivatives. For the fractional-order model, besides well-posedness and local stability, we prove the existence and uniqueness of non-negative solutions. Throughout the work, we compare the results graphically and present our conclusions. To represent graphically the solutions to the fractional model we use the modified trapezoidal method that involves the modified Euler method.
