Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization

‎This paper is devoted to study dynamical behaviors of the fractional-order BazykinBerezovskaya model and its discretization. The fractional derivative has been described in the Caputo sense. We show that the discretized system, exhibits more complicated dynamical behaviors than its corresponding fractional-order model. Specially, in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen. In the final part, some numerical simulations verify the analytical results.

Keywords:

Fractional-order dynamical system , Neimark-Sacker bifurcation , Flip bifurcation , chaos