Abstract
In this chapter, the dynamics of a modified predator-prey BB model with Allee effects and seasonal perturbation are investigated in some detail. In addition to the Hopf bifurcation, new bifurcation points are detected such as limit point cycle and period-doubling bifurcations and those by modeling the prey's growth rate and the predator efficiency by modified algebraic structures. The latter is based on noninteger elements giving more extended set of information for the predator-prey system compared to the structure-based-integer-order elements. Furthermore, numerical simulations show that the root mean square operator is a generator of the period doubling (PD) bifurcation. Moreover, our finding reveals that seasonal effects have a key significance on the dynamic properties of the BB prey-predator system. Indeed, in presence of such forcing effect, the system loses its original stability proprieties and vividly demonstrates complex chaos phenomenon.
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