The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cel...The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.展开更多
In this paper, we provide a Hopf bifurcation diagram of Lienard equation with a discrete delay, by using the (?) - D decomposition, one can determine the stability domain of the equilibrium and Hopf bifurcation curves...In this paper, we provide a Hopf bifurcation diagram of Lienard equation with a discrete delay, by using the (?) - D decomposition, one can determine the stability domain of the equilibrium and Hopf bifurcation curves in the parameter space.展开更多
文摘The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.
文摘In this paper, we provide a Hopf bifurcation diagram of Lienard equation with a discrete delay, by using the (?) - D decomposition, one can determine the stability domain of the equilibrium and Hopf bifurcation curves in the parameter space.
