Dynamics of a miRNA Model with Two Delays

MicroRNAs are a large class of post-transcriptional regulators of gene expression and they have important regulatory functions in basic cellular processes. In this paper, mathematical modeling and bifurcation analysis are combined to investigate in details the effect of time delays on the dynamics of a feedback system regulated with miRNA. Using the Hopf bifurcation theorem, we predict the occurrence of a limit cycle bifurcation for the time delay parameters. From the accomplished analytical and numerical results, it becomes clear that time delays have a destabilization dynamical role. Moreover, our numerical analysis suggests that amplitude of sustained miRNA oscillations depend essentially on the values of time delays.