Hopf bifurcation in time‐delayed gene expression model with dimers

Abstract

We study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive steady state and for the existence of the Hopf bifurcation. We check the influence of delay in transcription process on the model dynamics, and we formulate conditions determining the type of the Hopf bifurcation and stability of arising limit cycle.