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Monostability, bistability, periodicity and chaos in gene regulatory network

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Abstract

This letter gives a general review on the monostability, bistability, periodicity and chaos in gene regulatory network. Some simple motifs that generate monostability, bistability, periodicity and chaos are analytically and numerically reported. Further research directions of the nonlinear dynamics of gene regulatory network are discussed.

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References

  1. E.N. Olson, Science 313, 1922 (2006)

    Google Scholar 

  2. D.S. Bentabou, E.H. Davidson, Ann. Rev. Biophys. Biomol. Struct. 36, 191 (2007)

    Article  Google Scholar 

  3. J.M. Stuart, E. Segal, D. Koller, S.K. Kim, Science 302, 249 (2003)

    Article  ADS  Google Scholar 

  4. M. Laurent, N. Kellershohn, Trends Biochem. Sci. 24, 418 (1999)

    Article  Google Scholar 

  5. E. Mayr, The growth of biological thought: diversity, evolution and inheritance (Belknap Press, Cambridge, 1982)

  6. E.M. Ozbudak, M. Thattai, H.N. Lim, B.I. Shraiman, A. Oudenaarden, Nature 427, 737 (2004)

    Article  ADS  Google Scholar 

  7. C. Li, L. Chen, K. Aihara, Phys. Biol. 3, 37 (2006)

    Article  ADS  Google Scholar 

  8. P.E. Morant, Q. Thommen, F. Lemaire, C. Vandermoere, B. Parent, M. Lefranc, Phys. Rev. Lett. 102, 068104 (2009)

    Article  ADS  Google Scholar 

  9. X.P. Wu, M. Eshete, Commun. Nonlinear Sci. Numer. Simul. 16, 1073 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  10. Z. Levnajic, B. Tadic, Chaos 20, 033115 (2010)

    Article  ADS  Google Scholar 

  11. L. Chen, K. Aihara, IEEE Trans. Circuits Syst. I: Fund. Theor. Appl. 49, 602 (2002)

    Article  Google Scholar 

  12. R. Sakthivel, R. Raja, S.M. Anthoni, Phys. Scr. 82, 055009 (2010)

    Article  ADS  Google Scholar 

  13. F.X. Wu, IEEE Trans. Biomed. Circuits. Syst. 5, 391 (2011)

    Article  Google Scholar 

  14. L.P. Tian, Z.K. Shi, L.Z. Liu, F.X. Wu, IET Syst. Biol. 7, 214 (2013)

    Article  Google Scholar 

  15. Y. Han, X. Zhang, Y. Wang, Circuits Syst. Signal Process 34, 3161 (2015)

    Article  Google Scholar 

  16. Y. Wang, A. Yu, X. Zhang, Neural Comput. Appl. 23, 1217 (2013)

    Article  Google Scholar 

  17. X. Wan, L. Xu, H. Fang, F. Yang, Neurocomputing 124, 72 (2014)

    Article  Google Scholar 

  18. W. Zhang, J. Fang, Y. Tang, Neurocomputing 74, 2344 (2012)

    Article  Google Scholar 

  19. F. Ren, F. Cao, J. Cao, Neurocomputing 160, 185 (2015)

    Article  Google Scholar 

  20. H. Zang, T. Zhang, Y. Zhang, Appl. Math. Comput. 260, 204 (2015)

    MathSciNet  Google Scholar 

  21. J. Yu, M. Peng, Nonlinear Dyn. 86, 245 (2016)

    Article  Google Scholar 

  22. Y. Song, Y. Han, T. Zhang, Appl. Math. Comput. 243, 398 (2014)

    MathSciNet  Google Scholar 

  23. H. Liu, F. Yan, Z. Liu, Nonlinear Dyn. 76, 147 (2014)

    Article  Google Scholar 

  24. I. Zinovik, Y. Chebiryak, D. Kroening, IEEE Trans. Inf. Theory 56, 805 (2010)

    Article  Google Scholar 

  25. Y. Hori, T.H. Kim, S. Hara, Automatica 47, 1203 (2011)

    Article  Google Scholar 

  26. D. Fu, P. Tan, A. Kuznetsov, Y.I. Molkov, PLoS One 9, e90666 (2014)

    Article  ADS  Google Scholar 

  27. Z. Zhang, W. Ye, Y. Qian, Z. Zheng, X. Huang, G. Hu, PLoS One 7, e39355 (2012)

    Article  ADS  Google Scholar 

  28. C. Hsu, V. Jaquet, M. Gencoglu, A. Becskei, Cell Rep. 16, 1204 (2016)

    Article  Google Scholar 

  29. M.A. Leite, Y. Wang, Math. Biosci. Eng. 7, 83 (2010)

    Article  MathSciNet  Google Scholar 

  30. D.A. Oyarzun, M. Chaves, M. Hoff-Hoffmeyer-Zlotnik, J. Theo. Biol. 295, 139 (2012)

    Article  Google Scholar 

  31. W. Pan, Z. Wang, H. Gao, Y. Li, M. Du, Math. Biosci. 228, 100 (2010)

    Article  MathSciNet  Google Scholar 

  32. S. Mangan, U. Alon, PNAS 100, 11980 (2003)

    Article  ADS  Google Scholar 

  33. S. Ishihara, K. Fujimoto, T. Shibata, Genes Cells 10, 1025 (2005)

    Article  Google Scholar 

  34. W. Ye, X. Huang, X. Huang, P. Li, Q. Xia, G. Hu, Phys. Lett. A 374, 2521 (2010)

    Article  ADS  Google Scholar 

  35. D. Angeli, J.E. Ferrell, E.D. Sontag, PNAS 101, 1822 (2004)

    Article  ADS  Google Scholar 

  36. J.R. Kim, Y. Yoon, K.H. Cho, Biophys. J. 94, 359 (2008)

    Article  Google Scholar 

  37. T.S. Gardner, C.R. Cantor, J.J. Collins, Nature 403, 339 (2000)

    Article  ADS  Google Scholar 

  38. W. Pan, Z. Wang, H. Gao, X. Liu, Nature 11, 3170 (2010)

    Google Scholar 

  39. O. Cinquin, J. Demongeot, J. Theor. Biol. 216, 229 (2002)

    Article  Google Scholar 

  40. M. Bodnar, A. Bartlomiejczyk, Nonlinear Anal.: RWA 13, 2227 (2012)

    Article  Google Scholar 

  41. M. Xiao, J. Cao, Math. Biosci. 215, 55 (2008)

    Article  MathSciNet  Google Scholar 

  42. M. Andrecut, S.A. Kauffman, Phys. Lett. A 367, 281 (2007)

    Article  ADS  Google Scholar 

  43. C. Poignard, J. Math. Biol. 69, 335 (2014)

    Article  MathSciNet  Google Scholar 

  44. Y. Suzuki, M. Lu, E.B. Jacob, J.N. Onuchic, Sci. Rep. 6, 21037 (2016)

    Article  ADS  Google Scholar 

  45. Z. Levnajic, B. Tadic, Chaos 20, 033115 (2010)

    Article  ADS  Google Scholar 

  46. V. Sevim, P.A. Rikvold, J. Theor. Biol. 253, 323 (2008)

    Article  Google Scholar 

  47. Z. Zhang, W. Ye, Y. Qian, Z. Zheng, X. Huang, G. Hu, PLoS One 7, e39355 (2012)

    Article  ADS  Google Scholar 

  48. S. Jafari, J.C. Sprott, F. Nazarimehr, Eur. Phys. J. Special Topics 224, 1469 (2015)

    Article  ADS  Google Scholar 

  49. S. Jafari, V.T. Pham, S. Mohammad Reza Hashemi Golpayegani, M. Moghtadaei, S.T. Kingni, Int. J. Bifur. Chaos 26, 1650211 (2016)

    Article  Google Scholar 

  50. Q. Lai, T. Nestor, J. Kengne, X.W. Zhao, Chaos Soliton Fract. 107, 92 (2018)

    Article  ADS  Google Scholar 

  51. Q. Lai, S.M. Chen, Int. J. Bifur. Chaos 26, 1650177 (2016)

    Article  Google Scholar 

  52. F.L. Baldissera, E.R. Cury, J. Raisch, IEEE Trans. Autom Control 61, 18 (2016)

    Article  Google Scholar 

  53. R. Edwards, S. Kim, P. Driessche, J. Math. Biol. 62, 453 (2011)

    Article  MathSciNet  Google Scholar 

  54. L. Wang, R.Q Su, Z.G. Huang, X. Wang, W.X. Wang, C. Grebogi, Y.C. Lai, Nat. Commun. 7, 11323 (2006)

    Article  ADS  Google Scholar 

  55. A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014)

    Article  ADS  MathSciNet  Google Scholar 

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Correspondence to Qiang Lai.

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Lai, Q., Zhao, XW., Huang, JN. et al. Monostability, bistability, periodicity and chaos in gene regulatory network. Eur. Phys. J. Spec. Top. 227, 719–730 (2018). https://doi.org/10.1140/epjst/e2018-700132-8

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  • DOI: https://doi.org/10.1140/epjst/e2018-700132-8

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