ABSTRACT

The dynamical behaviour of two ecosystems of three species consisting of prey, intermediate predator and top predator that are still of current and recurring interests is investigated in this chapter. The classical integer-order derivatives in such models are replaced with the Atangana--Baleanu fractional derivative in the sense of Caputo. Existence and uniqueness of solution is established. Linear stability analysis is examined in a view to guide in the correct choice of parameters when numerically simulating the models. In the analysis, condition for a dynamic system to be locally asymptotically stable is provided. A range of chaotic and spatiotemporal phenomena that are obtained for different instances of $\alpha\in(0,1)$ are also given to justify the theoretical findings.