On oscillatory dynamics of small-RNAs-mediated two-gene regulatory networks

This paper studies oscillatory dynamics of two-gene regulatory networks which are mediated by small RNAs (sRNAs) and subject to multiple delays. First, stability of the positive fixed point and the existence of the local Hopf bifurcation are examined for sRNAs-mediated two-gene regulatory networks. Then sufficient conditions for periodic oscillation are established for such networks with multiple delays. Computer simulations are presented to illustrate the proposed results.

[1]  Jianwei Shen,et al.  Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs , 2009 .

[2]  S. Ruan,et al.  On the zeros of transcendental functions with applications to stability of delay differential equations with two delays , 2003 .

[3]  Fernando Corinto,et al.  Periodic oscillations in weakly connected cellular nonlinear networks , 2008, Proceedings. 2005 International Conference Physics and Control, 2005..

[4]  F. Corinto,et al.  Periodic Oscillations in Weakly Connected Cellular Nonlinear Networks , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Fang-Xiang Wu.  Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties. , 2011, IEEE transactions on biomedical circuits and systems.

[6]  Jinde Cao,et al.  Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays. , 2008, Mathematical biosciences.

[7]  Carsten Peterson,et al.  Transcriptional Dynamics of the Embryonic Stem Cell Switch , 2006, PLoS Comput. Biol..

[8]  Luonan Chen,et al.  Biomolecular Networks: Methods and Applications in Systems Biology , 2009 .

[9]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[10]  J. Mahaffy,et al.  Oscillations in a model of repression with external control , 1992, Journal of mathematical biology.

[11]  S. Gottesman.  Micros for microbes: non-coding regulatory RNAs in bacteria. , 2005, Trends in genetics : TIG.

[12]  Christian O'Reilly,et al.  Analyzing Oscillations for an $N$-node Recurrent Neural Networks Model With Time Delays and General Activation Functions , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Fernando Corinto,et al.  Periodic oscillations and bifurcations in cellular nonlinear networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Junjie Wei,et al.  Hopf bifurcation analysis in a model of oscillatory gene expression with delay , 2009, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[15]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[16]  B. Goodwin.  Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.