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

Abstract

‎This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization‎. ‎The fractional derivative has been described in the Caputo sense‎. ‎We show that the discretized system‎, ‎exhibits more complicated dynamical behaviours 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 simulation verify the analytical results‎.