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Numerical bifurcation control of Mackey-Glass system. (English) Zbl 1221.93235

Summary: A mathematical physiological model, the Mackey – Glass system of a delay differential equation, is considered. With a greater delay, a periodic solution arises, which characterizes the disease of chronic granulocytic leukemia (CGL). To treat such disease, a blood transfusion feedback control is considered, from the point of view of mathematical control. By using a nonstandard finite-difference (NSFD) scheme to the control system, we obtain a numerical discrete system and analyze its Neimark – Sacker and fold bifurcations. The results imply that the condition of the illness could be relieved by transfusing blood to the patient, if the control is a delay control. Finally, the effectiveness of the control are illustrated by several numerical simulations.

MSC:

93D15 Stabilization of systems by feedback
92C30 Physiology (general)
34K18 Bifurcation theory of functional-differential equations
37N25 Dynamical systems in biology
93B52 Feedback control
92-08 Computational methods for problems pertaining to biology
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References:

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