ANALYSIS OF A DISCRETIZED FRACTIONAL-ORDER PREY–PREDATOR MODEL UNDER WIND EFFECT

Abstract While constructing mathematical models, scientists usually consider biotic factors, but it is crystal-clear that abiotic factors, such as wind, are also important as biotic factors. From this point of view, this paper is devoted to the investigation of some bifurcation properties of a fractional-order prey–predator model under the effect of wind. Using fractional calculus is very popular in modelling, since it is more effective than classical calculus in predicting the system’s future state and also discretization is one of the most powerful tools to study the behaviour of the models. In this paper, first of all, the model is discretized by using a piecewise discretization approach. Then, the local stability of fixed points is considered. We show using the centre manifold theorem and bifurcation theory that the system experiences a flip bifurcation and a Neimark–Sacker bifurcation at a positive fixed point. Finally, numerical simulations are given to demonstrate our results.