Dynamics of a Neutrophil Model with State Feedback Control of Time Delay

Abstract

The complex periodical transition phenomena of the neutrophil model are investigated underlying delay feedback control strategy. By application of DDE-Biftool software, which develops an artificial technique to compute codimension 1 bifurcation of periodical solutions with singularity, both of the route of P-2 solutions to homoclinic bifurcation and the period-doubling bifurcation phenomena are investigated. The Bautin bifurcation point departs the subcritical Hopf point from the supercritical Hopf point. The Bautin point observed within the first Hopf point is the intersection point of the Hopf line with the limit point cycle bifurcation line; however, the Bautin point discovered with the second Hopf point is distinct via a special scheme as the lineup of periodical solution circle broken. The numerical simulation results aid to provide a helpful understanding in periodical oscillation phenomena of the neutrophil model.