University of Tabriz Computational Methods for Differential Equations 2345-3982 6 2 2018 04 01 Discretization of a fractional order ratio-dependent functional response predator-prey model, bifurcation and chaos 248 265 7182 EN Razie Shafeii Lashkarian Department of Basic science, Hashtgerd Branch, Islamic Azad University, Alborz, Iran Dariush Behmardi Sharifabad Department of Mathematics, Alzahra university, Tehran, Iran Journal Article 2017 01 30 This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is not more of fractional order, exhibits much richer dynamical behavior than its corresponding fractional order model. Specially, in the discretized system, many types of bifurcations (transcritical, flip, Neimark-Sacker) and chaos may happen, however, the local analysis of the fractional-order counterpart, only deals with the stability (unstability) of the equilibria. Finally, some numerical simulations are performed by MATLAB, to support our analytic results. https://cmde.tabrizu.ac.ir/article_7182_b7136c735af5518730e4553adfc20658.pdf