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No Access Submitted: 26 October 2011 Accepted: 02 December 2011 Published Online: 22 December 2011

Exponential cluster synchronization of impulsive delayed genetic oscillators with external disturbances

Chaos 21, 043137 (2011); https://doi.org/10.1063/1.3671609
Wenbing Zhang1, a), Yang Tang2,3,4, b), Jian-an Fang1, c), and Wu Zhu1, d)
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ABSTRACT
This paper investigates the problem of the exponential cluster synchronization of coupled impulsive genetic oscillators with external disturbances and communication delay. Based on the Kronecker product, some new cluster synchronization criteria for coupled impulsive genetic oscillators with attenuation level are derived. The derived results are related to the impulsive strength, and the derived results also indicate that the maximal allowable bound of time delay is inversely proportional to the decay rate, the decay rate is proportional to the couple strength, the maximal allowable bound of time delay is proportional to attenuation level, and the attenuation level is inversely proportional to the couple strength. Moreover, the case when the feedback have different self-delay is also investigated. Finally, numerical examples are given to illustrate the effectiveness of the derived results.

ACKNOWLEDGMENTS

The authors are grateful to the Editor and anonymous reviewers for their constructive comments and suggestions that helped to improve the content as well as the quality of the manuscript.
This paper was partially supported by the National Science Foundation of PR China (60874113), the Key Creative Project of Shanghai Education Community (09ZZ66), the Research Fund for the Doctoral Program of Higher Education (200802550007), the Alexander von Humboldt Foundation of Germany and the Key Basic Research Project of Shanghai (09JC1400700) and the China Postdoctoral Science Foundation (2011M501040).

REFERENCES
Section:
Previous sectionNext section

  1. 1. S. Huang, J. Mol. Med. 77, 6 (1999). https://doi.org/10.1007/s001099900023 , Google ScholarCrossref
  2. 2. S. A. Kauffman, J. Theor. Biol. 22, 3 (1969). https://doi.org/10.1016/0022-5193(69)90015-0 , Google ScholarCrossref
  3. 3. G. Chesi and Y. S. Hung, Automatica 44, 9 (2008). https://doi.org/10.1016/j.automatica.2008.01.030 , Google ScholarCrossref
  4. 4. C. Li, L. Chen, and K. Aihara, IEEE Trans. Circuits Syst. I. 53, 11 (2006). https://doi.org/10.1109/TCSI.2006.883882 , Google ScholarCrossref
  5. 5. L. Chen and K. Aihara, IEEE Trans. Circuits Syst. I. 49, 5 (2002). https://doi.org/10.1109/TCSI.2002.1001949 , Google ScholarCrossref
  6. 6. C. Li, L. Chen, and K. Aihara, Phys. Biol. 3, 1 (2006). https://doi.org/10.1088/1478-3975/3/1/004 , Google ScholarCrossref
  7. 7. Z. Wang, H. Gao, J. Cao, and X. Liu, IEEE Trans. Nanobiosci. 7, 2 (2008). https://doi.org/10.1109/TNB.2008.2000746 , Google ScholarCrossref
  8. 8. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, and H. Okamura, Science 302, 5649 (2003). https://doi.org/10.1126/science.1089287 , Google ScholarCrossref
  9. 9. L. Scardovi, M. Arcak and E. D. Sontag, IEEE Trans. Autom. Control 55, 6 (2010). https://doi.org/10.1109/TAC.2010.2041974 , Google ScholarCrossref
  10. 10. Y. Tang, Z. Wang, and J. Fang, Chaos 19, 013112 (2009). https://doi.org/10.1063/1.3068350 , Google ScholarScitation
  11. 11. Y. Tang, Z. Wang, W. K. Wong, J. Kurths, and J. Fang, Chaos 21, 025114 (2011). https://doi.org/10.1063/1.3595701 , Google ScholarScitation
  12. 12. R. Wang and L. Chen, J. Biol. Rhythms 20, 3 (2005). https://doi.org/10.1177/0748730405275653 , Google ScholarCrossref
  13. 13. A. Kuznetsov, M. Kærn, and N. Kopell, SIAM J. Appl. Math. 65, 2 (2004). https://doi.org/10.1137/S0036139903436029 , Google ScholarCrossref
  14. 14. D. Gonze, S. Bernard, C. Waltermann, A. Kramer, and H. Herzel, Biophys J. 89, 1 (2005). https://doi.org/10.1529/biophysj.104.058388 , Google ScholarCrossref
  15. 15. J. Lu and D. W. C. Ho, IEEE Trans. Syst. Man. Cybern.-B. 40, 2 (2010). https://doi.org/10.1109/TSMCB.2009.2031199 , Google ScholarCrossref
  16. 16. W. He and J. Cao, IEEE Trans. Neural Networks. 21, 4 (2010). https://doi.org/10.1109/TNN.2009.2039803 , Google ScholarCrossref
  17. 17. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, England, 2001). Google ScholarCrossref
  18. 18. A. Arenas, A. Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. 469, 3 (2008). https://doi.org/10.1016/j.physrep.2008.09.002 , Google ScholarCrossref
  19. 19. T. Oguchi, H. Nijmeijer, and T. Yamamoto, Chaos 18, 037108 (2008). https://doi.org/10.1063/1.2952450 , Google ScholarScitation
  20. 20. N. Buric, I. Grozdanoviandc, and N. Vasovic, Chaos Solitons Fractals 36, 4 (2008). https://doi.org/10.1016/j.chaos.2006.09.061 , Google ScholarCrossref
  21. 21. J. Lu, D. W. C. Ho, and J. Kurths, Phys. Rev. E 80, 6 (2009). https://doi.org/10.1103/PhysRevE.80.066121 , Google ScholarCrossref
  22. 22. P. Li and J. Lam, Asian J. Control 13, 5 (2011). https://doi.org/10.1002/asjc.360 , Google ScholarCrossref
  23. 23. U. Münz, A. Papachristodoulou, and F. Allgöwer, Automatica 46, 8 (2010). https://doi.org/10.1016/j.automatica.2010.04.008 , Google ScholarCrossref
  24. 24. Y. Tang, S. Y. S. Leung, W. K. Wong, and J. Fang, Neurocomputing 73, 10–12 (2010). https://doi.org/10.1016/j.neucom.2010.02.010 , Google ScholarCrossref
  25. 25. J. Lu, D. W. C. Ho, J. Cao, and J. Kurths, IEEE Trans. Neural Networks 22, 2 (2011). https://doi.org/10.1109/TNN.2010.2101081 , Google ScholarCrossref
  26. 26. J. Lu, D. W. C. Ho, and J. Cao, Automatica 46, 6 (2010). https://doi.org/10.1016/j.automatica.2010.04.005 , Google ScholarCrossref
  27. 27. Z. Yang and D. Xu, IEEE Trans. Circuits Syst.-II: Express Briefs 52, 8 (2005). https://doi.org/10.1109/TCSII.2005.849032 , Google ScholarCrossref
  28. 28. E. D. Sontag, Eur. J. Control 11, 4–5 (2005). https://doi.org/10.3166/ejc.11.396-435 , Google ScholarCrossref
  29. 29. V. S. Vaidhyanathan, Regulation and Control Mechanisms in Biological Systems (PTR Prentice Hall, Englewood Cliffs, NJ, 1993). Google Scholar
  30. 30. P. Li and J. Lam, IEEE Acm Trans. Comput. Biol. 8, 1 (2011). https://doi.org/10.1109/TCBB.2011.7 , Google ScholarCrossref
  31. 31. J. Kruger, Neuronal Cooperativity (Springer, New York, 1991). Google ScholarCrossref
  32. 32. E. Vaadia and A. Acrtsen, “Coding and Computation in the Cortex: Single Neuron Activity and Cooperative Phenomena,” in Information Processing in the Cortex: Experiments and Theory, edited by A. Acrtsen and V. Braitemberg (Berlin, Springer, 1992), pp. 81–121. Google ScholarCrossref
  33. 33. Z. Ma and Z. Liu, Chaos 16, 023103 (2006). https://doi.org/10.1063/1.2184948 , Google ScholarScitation
  34. 34. I. Belykh, V. Belykh, K. Nevidin, and M. Hasler, Chaos 13, 1 (2003). https://doi.org/10.1063/1.1514202 , Google ScholarScitation
  35. 35. V. N. Belykh, I. Belykh, M. Hasler, and K. V. Nevidin, Int. J. Bifurcation Chaos 13, 4 (2003). https://doi.org/10.1142/S0218127403006923 , Google ScholarCrossref
  36. 36. J. Cao and L. Li, Neural Networks 22, 4 (2009). https://doi.org/10.1016/j.neunet.2009.03.006 , Google ScholarCrossref
  37. 37. C. Wu and L. O. Chua, IEEE Trans. Circuits Syst. I. 42, 8 (1995). https://doi.org/10.1109/81.404047 , Google ScholarCrossref
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