STABILITY AND BIFURCATION ANALYSIS OF A SIMPLE DELAYED p53-Mdm2 GENE NETWORK MODEL WITH DIFFUSION

Abstract

p53 is a star protein in cancer biology, and its oscillatory dynamics have received much attention. However, most studies do not consider spatial effects. For this reason, we introduce the diffusion term in a classical p53-Mdm2 autoregulatory loop model. First, the equation is linearized at the positive equilibrium so that we can discuss the local asymptotic stability of this equilibrium. By taking the delay as a bifurcation parameter, the positive equilibrium transitions from stable to unstable and occurs a Hopf bifurcation. Second, we determine the stability of the bifurcating period solution by using a multiple time scales approach. Finally, the theoretical analysis is verified by the numerical simulations. Our study contributes to providing new insight in the controlling of p53 dynamics.