Abstract

In this paper, the nonlinear dynamics of a modified predator-prey algebraic model with strong Allee effect and seasonally perturbation are analysed. It is shown that the modified algebraic structure where the prey's growth rate and the predator efficiency are described by non-integer order polynomials gives more set of information then the classical one. Thus, it is proved that new bifurcation points are occurred such as Limit point cycle and period-doubling bifurcations. In addition, for the seasonally perturbed system, a chaotic behavior occurs with a high positive Lyapunov exponent.

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