We consider a model for gene expression with one or two time delays and diffusion. The local stability and delay-induced Hopf bifurcation are investigated. We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.
Yahong Peng. Tonghua Zhang. "Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay." Abstr. Appl. Anal. 2014 (SI01) 1 - 9, 2014. https://doi.org/10.1155/2014/738682