Chaotic behaviour in system of noninteger-order ordinary differential equations

The intra-specific relation two predators and a prey dependent food chain system is considered in this paper. To explore the dynamic richness of such system, we replace the classical time-derivative with either the Caputo or the Atangana-Baleanu fractional derivative operators. Two notable numerical schemes for the approximation of such derivatives are formulated. Local and global stability analysis are investigated to ensure the correct choice of the biologically meaning parameters. The condition for occurrence of the Hopf-bifurcation is also observed. We justify the performance of these schemes by reporting their absolute error when applied to nonlinear fractional differential equations. In addition, numerical simulations with different α values and experimented parameter values confirm the analytical results shows that modelling with fractional derivative could give rise to a more richer chaotic dynamics.