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Glycolysis model has been considered by Caputo fractional derivative. We give the topological classifications of fixed points of this model. Then, we show analytically that under certain parametric conditions fractional order glycolysis model underlies a Neimark-Sacker (NS) bifurcation and Flip bifurctaion. By using central manifold and bifurcation theory, we confirm the existence and direction of both NS and Flip bifurcations. To reinforce our analytical findings, we perform numerical simulations that include bifurcations, phase portraits, periodic orbits, invariant closed cycles, abrupt emergence of chaos and abrupt elimination of chaos. At the end, OGY method is applied to eliminate chaotic trajectories of the system.
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