A chaos study of fractal–fractional predator–prey model of mathematical ecology

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on fractal–fractional Atangana–Baleanu (AB) and Caputo operators, we present a newly developed system of differential equations for the predator–prey system. Our study utilized the fixed point postulate to investigate the uniqueness and existence of solutions. Additionally, Ulam's type of stability of the proposed model is established with the help of nonlinear functional analysis. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyze its behavior. The generalized non-linear system with fractal–fractional Atangana–Baleanu (AB) and Caputo non-integer operators have been solved numerically via the Toufik–Atangana (TA) scheme respectively. We have demonstrated the applicability and effectiveness of these methods by analyzing numerical simulations for the fractal–fractional predator–prey ecological model and the numerical simulation has been calculated by MATLAB programming.