Under gamma irradiation, p53 gene regulatory network is able to exhibit three different modes, namely low state, oscillations, and high state. There are experimental studies demonstrating that oscillatory behaviour of p53 is due to the interaction between upstream mediator of p53, i.e. ATM, and a negative feedback loop formed by Wip1 with that upstream. By proposing a canonical model based on ordinary differential equations made up of polynomial type birth and death terms, we show mathematically that the simple interaction between ATM and Wip1 is indeed able to exhibit three different behaviours relevant to DNA damage response of p53 network. We further carry out bifurcation analysis on the model with the aim of investigating the mutations such as Wip1 overexpression and ATM deficiency. Based on the proposed canonical model, we show that Wip1 is an important target for curing these types of mutations.