Complex behavior of a miRNA model with three delays

S.G. Nikolov

Abstract: MiRNAs are kinds of noncoding RNAs which can regulate the activity and stability of the target mRNAs through base-pair matching. In this paper, a nonlinear mathematical model with three discrete time delays is used to investigate the dynamics of the gene expression regulated by the miRNA. Using a new theoretical approach and Hopf bifurcation theorem it is predicted the occurrence of a limit cycle bifurcation for the time delay parameters. From the accomplished analytical results and numerical simulations, it is becomes clear that time delays have destabilization dynamical role. Moreover, for some specific numerical values of the model parameters a complex (non-regular) behavior of the model is demonstrated.

Keywords: Andronov-Hopf bifurcation; complex behavior; miRNA; time delay

Date published: 2013-12-09