Abstract
This present work, we discuss the complex dynamical nature of the three species prey–predator system in presence of scavenger with fractional order. A discretization process is applied to obtain its discrete version and the impact of the scavenger on the ecosystem is discussed. Firstly, existence and local stability of the equilibria state of the model are addressed. The presences of Flip bifurcation and Neimark-Sacker bifurcation around boundary and coexistence equilibrium states are studied by using bifurcation theory. The trajectories and phase plane diagrams are plotted for biologically meaningful sets of parameter values. Numerical simulations for the effect of step size and fractional order parameters of the system are performed, on the first part to demonstrate the analytical results and on the second part revealing new motivating the dynamics behaviors of the scavenger model including period-doubling cascades (flip), periods—2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24 and 32 orbits, invariant cycles, a chaotic attractors, and the rich dynamic behaviors of the discretized model is exhibited.
Published Version
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