Mathematical Biology Seminar: Xihui (Eric) Lin

Abstract

In this talk, I'll introduce Kuang and Beretta's method to determine the stability of equilibria for delay differential equations (DDEs).  Based on this method and some numerical results from some classic models(predator-prey, HIV, CTL-response to HLTV-I infection),  I am going to show you that time lags could lead to stability switch of steady state, and multiple stable periodic solutions in these models exist. In addition, global behaviors of Hopf bifurcations in these models are simple and correspondent to the behavior of characteristic roots with positive real part in the characteristic equation. A Hopf bifurcation in these model starts at some time delay (say tau1), where there is a pair of characteristic roots passing the imaginary axis to the right, and ends right at the next time delay(say tau2), where there is a pair of characteristic roots passing the imaginary axis to the left.