137
Views
19
CrossRef citations to date
0
Altmetric
Original Articles

Limit cycles in piecewise-affine gene network models with multiple interaction loops

&
Pages 119-130 | Received 23 Feb 2009, Accepted 09 Jun 2009, Published online: 08 Jan 2010

References

  • Casey , R , de Jong , H and Gouzé , JL . 2006 . Piecewise-Linear Models of Genetic Regulatory Networks: Equilibria and Their Stability . Journal of Mathematical Biology , 52 ( 1 ) : 27 – 56 .
  • de Jong , H . 2002 . Modeling and Simulation of Genetic Regulatory Systems: A Literature Review . Journal of Computational Biology , 9 ( 1 ) : 67 – 103 .
  • de Jong , H , Gouzé , JL , Hernandez , C , Page , M , Sari , T and Geiselmann , J . 2004 . Qualitative Simulation of Genetic Regulatory Networks using Piecewise-Linear Models . Bulletin of Mathematical Biology , 66 ( 2 ) : 301 – 340 .
  • de Jong , H , Geiselmann , J , Batt , G , Hernandez , C and Page , M . 2004 . Qualitative Simulation of the Initiation of Sporulation in Bacillus Subtilis . Bulletin of Mathematical Biology , 66 ( 2 ) : 261 – 300 .
  • Glass , L . 1975 . Combinatorial and Topological Methods in Nonlinear Chemical Kinetics . Journal of Chemical Physics , 63 : 1325 – 1335 .
  • Glass , L and Pasternack , JS . 1978 . Prediction of Limit Cycles in Mathematical Models of Biological Oscillations . Bulletin of Mathematical Biology , 40 : 27 – 44 .
  • Glass , L and Pasternack , JS . 1978 . Stable Oscillations in Mathematical Models of Biological Control Systems . Journal of Mathematical Biology , 6 : 207 – 223 .
  • Edwards , R . 2000 . Analysis of Continuous-Time Switching Networks . Physica D , 146 : 165 – 199 .
  • Farcot , E . 2006 . Geometric Properties of Piecewise Affine Biological Network Models . Journal of Mathematical Biology , 52 ( 3 ) : 373 – 418 .
  • Farcot , E and Gouzé , J-L . 2006 . Periodic Solutions of Piecewise Affine Gene Network Models: the Case of a Negative Feedback Loop . INRIA Research Report , RR-6018, https://hal.inria.fr/inria-00112195
  • Farcot , E and Gouzé , J-L . 2008 . A Mathematical Framework for the Control of Piecewise-Affine Models of Gene Networks . Automatica , 44 ( 9 ) : 2326 – 2332 .
  • Farcot , E and Gouzé , J-L . 2009 . Periodic Solutions of Piecewise Affine Gene Network Models with Non- Uniform Decay Rates: the Case of a Negative Feedback Loop . Acta Biotheoretica , to appear
  • Gouzé , JL and Sari , T . 2003 . A Class of Piecewise Linear Differential Equations Arising in Biological Models . Dynamical systems , 17 : 299 – 316 .
  • Kauffman , SA . 1993 . The origins of order , New York : Oxford University Press .
  • Li , Q and Yang , X-S . 2006 . Chaotic Dynamics in a Class of Three Dimensional Glass Networks . Chaos 16 , 033101
  • Mestl , T , Plahte , E and Omholt , SW . 1995 . Periodic Solutions of Piecewise-linear Differential Equations . Dynamics and Stability of Systems , 10 ( 2 ) : 179 – 193 .
  • Murray , JD . 1989 . Mathematical Biology , Berlin : Springer .
  • Ropers , D , de Jong , H , Page , M , Schneider , D and Geiselmann , J . 2006 . Qualitative Simulation of the Carbon Starvation Response in Escherichia Coli . Biosystems , 84 ( 2 ) : 124 – 152 .
  • Smith , H . 1986 . Cooperative Systems of Differential Equations with Concave Nonlinearities . Nonlinear Analysis , 10 : 1037 – 1052 .
  • Thomas , R and D'Ari , R . 1990 . Biological Feedback , Boca Raton, FL : CRC-Press .
  • Wang , Z , Gao , H , Cao , J and Liu , X . 2008 . On Delayed Genetic Regulatory Networks with Polytopic Uncertainties: Robust Stability Analysis . IEEE Transactions on NanoBioscience , 7 ( 2 ) : 154 – 163 .
  • Wang , Z , Yang , F , Ho , DWC , Swift , S , Tucker , A and Liu , X . 2008 . Stochastic Dynamic Modeling of Short Gene Expression Time Series Data . IEEE Transactions on NanoBioscience , 7 ( 1 ) : 44 – 55 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.