Bifurcation dynamics of the modified physiological model of artificial pancreas with insulin secretion delay

In this paper, we modify the original physiological model of artificial pancreas by introducing the insulin secretion time delay. The non-resonant double Hopf bifurcation is analyzed by the Center Manifold Theorem and Normal Form Method. Numerical results supporting the theoretical analysis are presented in some typical parameter regions. It is shown that the critical value of technological delay and the area of death island of the non-resonant double Hopf bifurcation in the modified model are far less than those in the original model. This implies that when the secretion delay appears, the smaller technological delay can induce the double Hopf bifurcation. In addition, the region IV with complex coexisting bi-stability also decreases sharply. Furthermore, the rich dynamics such as various period, quasi-period and chaotic behaviors are found when some key parameters are changed. The obtained results can have important theoretical guidance for the diagnosis and treatment of diabetes patients.