Numerical bifurcation control of Mackey-Glass system

作者：Su Huan^*; Ding Xiaohua; Li Wenxue

来源：Applied Mathematical Modelling, 2011, 35(7): 3460-3472.

DOI：10.1016/j.apm.2011.01.009

• Mackey-Glass system
• Feedback control
• Chronic granulocytic leukemia
• Nonstandard finite-difference scheme

In this paper, a mathematical physiological model, 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.

• 出版日期2011-7
• 单位哈尔滨工业大学