Dynamical behavior of a fractional three-species food chain model

Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

“…5a) and it occurs (Fig. 5b) at a 0 ≈ 1.69 for the fractional order m = 0.97 [20]. If we consider our global parameter set of Example 4 with the same initial values as in [20] and draw similar bifurcations (Figs.…”

“…Alidousti and Ghahfarokhi [20] proved the following results regarding positivity and boundedness of the solutions of system (4).…”

“…where v 3 > d 3 c 3 and v 1 > a 1 . Local and global stability results for the equilibrium points E 0 , E 1 and E 2 are given in [20]. In the following, we give local and global stability results of E * only.…”

“…4 demonstrates that solutions starting from different initial values converge to the equilibrium point E * = (11.3623, 6.3158, 0.4162) of (3) for different fractional orders, m = 0.65, 0.75, 0.85 , and also for the integer order, m = 1 , depicting the global stability of the interior equilibrium point for fractional order as well as integer order. Example 5: Here we consider the exact parameter set and initial value as in Alidousti and Ghahfarokhi [20] and reproduce their bifurcation diagrams ( Figs. 5a and 5b) with respect to the same growth rate parameter of prey (here it is a 0 ) in the same range [1.6, 2.1] for the orders m = 1 and m = 0.97 .…”

“…5a and 5b) with respect to the same growth rate parameter of prey (here it is a 0 ) in the same range [1.6, 2.1] for the orders m = 1 and m = 0.97 . As shown in [19,20], the system (3) exhibits complex chaotic dynamics through period-doubling bifurcation. The first perioddoubling bifurcation occurs at a 0 ≈ 1.66 for the integer order m = 1.0 ( Fig.…”