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Abstract and Applied Analysis
Volume 2014, Article ID 738682, 9 pages
Research Article

Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay

1Department of Mathematics, Donghua University, Shanghai 200051, China
2Department of Mathematics, Swinburne University of Technology, Melbourne, VIC 3122, Australia

Received 24 February 2014; Accepted 13 March 2014; Published 14 April 2014

Academic Editor: Weiming Wang

Copyright © 2014 Yahong Peng and Tonghua Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.