Relation between intersection of nullclines and periodic solutions in a differential equations of p53 oscillator

We consider a simple mathematical model that suggests emergence of oscillations in p53 and Mdm2 protein levels in response to stress signal. Intracellular activity of the p53 protein is regulated by a transcriptional target, Mdm2, through a feedback loop. The model is classified in five cases with respect to intersection of nullclines. In each case occurrence(or not) of the limit cycle is investigated.