Abstract
<jats:p>Neimark-Sacker bifurcation theory is used to analyze a differential equation system. A three dimensionel continuous time system is investigated here. Generally, forward Euler scheme is used for discretization from continuous time system to discrete time system. But, in this study Nonstandard Finite Difference (NSFD) scheme is applied to discrete the continuous time system to discrete time system. After that, we examine topological structure of equation. Then, we give the conditions of local stability of this system around feasible fixed point. After, we show analitically that discretized system undergoes Neimark-Sacker bifurcation when one of the system parameter varies near its critical value. We confirm the existence of Neimark-Sacker bifurcation via explicit Flip and Neimark-Sacker bifurcation criterion. And we determine the direction of bifurcation with the help of center monifold theory and bifurcation theory. We carry out numerical simulation to approve our analitical findings.</jats:p>