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Cancer is the leading cause of death worldwide. The p53 gene play important role in the suppression of tumours. p53 is the central protein in the DNA damage response and is a part of a complex gene regulatory network. This network integrates a variety of stress signals to produce the up-regulation of active p53 and elicit apoptosis, growth arrest and DNA damage repair. In this paper, we construct a discrete model of regulatory network involving p53 and its inhibitor Mdm2, and use it to examine the effect of stresses that trigger p53. In response to stress the model demonstrates a variety of specific output behaviours of steady states with high levels of Mdm2 and cycle (oscillation) with low or high p53 levels.