By using a mathematical representations of the microRNA (miRNA) interaction cancer network we derive explicit conditions on how the dynamics of a time delay model of the interaction between the miRNA-17-92 cluster and the transcription factors E2F and Myc depends on systems parameters. Our analysis reveals the complex behaviour of the system. We compute the occurrence of a limit cycle after an Andronov-Hopf bifurcation for the time delay parameter and show that the analytical results agree with numerical simulations, i.e. the time delay has a stabilization role.
Key words: microRNA regulation, time delay model, stability analysis