Stability and Neimark-Sacker Bifurcation Analysis in a Genetic Network with Delay
Feng Liu*,†, Xiang Yin*, Zhe Zhang*, and Fenglan Sun**
*School of Automation, China University of Geosciences
No.388 Lumo Road, Wuhan 430074, China
**Research Center of System Theory and Application, Chongqing University of Posts and Telecommunications
No.2 Chongwen Road, Nanan District, Chongqing 400065, China
-  J. K. Hale and S. V. Lunel, “Introduction to Functional Differential Equations,” Springer-Verlag, 1993.
-  K. Gu, V. Kharitonov, and J. Chen, “Stability of Time-Delay Systems,” Birkhäuser Basel , 2003.
-  S. Haykin, “Neural Networks,” Prentice Hall, 1999.
-  S. Niculescu, “Delay Effects on Stability: A Robust Control Approach,” Springer-Verlag, 2001.
-  L. Chen and K. Aihara, “Stability of genetic regulatory networks with time delay,” IEEE Trans. Circuits & Systems I, Vol.49, No.5, pp. 602-608, 2002.
-  M. Xiao and J. Cao, “Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays,” Mathematical biosciences, Vol.215, No.1, pp. 55-63, 2008.
-  F. Wu, “Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties,” IEEE Trans. Biomedical Circuits and Systems, Vol.5, No.4, pp. 391-398, 2011.
-  W. Wang and S. Zhong, “Stochastic stability analysis of uncertain genetic regulatory networks with mixed time-varying delays,” Neurocomputing, Vol.82, pp. 143-156, 2012.
-  P. Smolen, D. A. Baxter, and J. H. Byrne, “Modeling transcriptional control in gene networks-methods, recent results, and future,” Bull. Math. Biol., Vol.62, pp. 247-292, 2007.
-  C. Zhang, M. Liu, and B. Zheng, “Hopf bifurcation in numerical approximation of a class delay differential equations,” Appl. Math. Comput., Vol.146, pp. 335-349, 2003.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.