Stability and bifurcation analysis of a gene expression model with small RNAs and mixed delays

Abstract

Abstract This paper investigates a gene expression model, which is mediated by sRNAs (small RNAs) and includes discrete and distributed delays. We take both the strong and weak kernel forms of distributed delay into consideration. The discrete time delay is chosen as the bifurcation parameter. By analyzing the distribution of characteristic values, we obtain the sufficient conditions of stability and examine the existence of periodic oscillations. When the discrete time delay is small and not greater than the threshold, the equilibrium of the gene expression model is asymptotically stable. When the bifurcation parameter exceeds the critical value, the model can produce limit cycles. Finally, numerical simulations are implemented to verify the correctness of our theoretical results.

Keywords

• Hopf bifurcation
• Local stability
• Periodic oscillation
• Distributed delay
• Genetic expression model