Hopf bifurcation analysis in a fractional-order survival red blood cells model and PDα control

Abstract

In this paper, we put forward a fractional-order survival red blood cells model and study the dynamics through the Hopf bifurcation. When the delay transcends the threshold, a series of Hopf bifurcations occur at the positive equilibrium. Then, a fractional-order Proportional and Derivative (PDα) controller is applied to the proposed model for the Hopf bifurcation control. It is discovered that by setting proper parameters, the PDα controller can delay or advance the onset of Hopf bifurcations. Therefore the Hopf bifurcation of the fractional-order survival red blood cells model becomes controllable to achieve desirable behaviors. Finally, numerical examples are presented to demonstrate the theoretical analysis.