The recent experiments on the dynamics of a common biological network motif, p53-Mdm2 feedback loop in population and individual cells shows two different kinds of oscillatory behaviors, namely the damped and sustained oscillations, for the activities of p53 and Mdm2 proteins in response to DNA damage. By exploiting the nonlinear dynamics in the negative feedback loop and through analyzing the dynamical relation between the DNA damage and the activities of p53 and Mdm2 proteins, we propose a nonlinear dynamical model to describe the oscillatory behaviors for the activities of p53 and Mdm2 proteins both in individual and in population of cells in a self-consistent and unified way.