Abstract
A new mathematical delayed model with two discrete time delays is presented for description of the behavior of the blood glucose regulation system. This study includes glucagon as a third effective variable. Sufficient conditions are obtained for local stability and the existence of Hopf bifurcation caused by variation of delays as the bifurcation parameters. Also we find some explicit formulas to determine the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions via the theory of normal form and center manifolds. Moreover, some numerical diagrams are illustrated for better understanding of the theoretical results.
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