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Synchronization and chaos control by quorum sensing mechanism

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Abstract

Diverse rhythms are generated by thousands of oscillators that somehow manage to operate synchronously. By using mathematical and computational modeling, we consider the synchronization and chaos control among chaotic oscillators coupled indirectly but through a quorum sensing mechanism. Some sufficient criteria for synchronization under quorum sensing are given based on traditional Lyapunov function method. The Melnikov function method is used to theoretically explain how to suppress chaotic Lorenz systems to different types of periodic oscillators in quorum sensing mechanics. Numerical studies for classical Lorenz and Rössler systems illustrate the theoretical results.

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References

  1. Perora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  2. Guo, L., Xu, Z.: Hölder continuity of two types of generalized synchronization manifold. Chaos 18, 033134 (2008)

    Article  MathSciNet  Google Scholar 

  3. Mahmoud, G.M., Mahmoud, E.E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn. 62, 875–882 (2010)

    Article  MATH  Google Scholar 

  4. Zhou, J., Wu, Q., Xiang, L.: Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization. Nonlinear Dyn. 69, 1393–1403 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Odibat, Z.M.: Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dyn. 60, 479–487 (2012)

    Article  MathSciNet  Google Scholar 

  6. Guo, L., Xu, Z., Hu, M.: Adaptive projective synchronization with different scaling factors in networks. Chin. Phys. B 17, 4067–4072 (2008)

    Article  Google Scholar 

  7. Huygens, C.: Oeuvres complètes de Christiaan Huygens vol. 17. Nijhoff, The Hague (1932)

    Google Scholar 

  8. Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge, Cambridge University Press (2001)

    Book  Google Scholar 

  9. Vladimirov, A.G., Kozyreff, G., Mandel, P.: Synchronization of weakly stable oscillators and semiconductor laser arrays. Europhys. Lett. 61, 613–619 (2003)

    Article  Google Scholar 

  10. Wiesenfeld, K., Colet, P., Strogatz, S.: Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett. 76, 404–407 (1996)

    Article  Google Scholar 

  11. Boccaletti, S., Grebogi, C., Lai, Y.C., Mancini, H., Maza, D.: The control of chaos: theory and applications. Phys. Rep. 329, 103–197 (2000)

    Article  MathSciNet  Google Scholar 

  12. Chen, G., Dong, X.: From Chaos to Order: Perspectives Methodologies and Applications. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  13. Lu, J., Wu, X., Lü, J.: Synchronization of a unified chaotic system and the application in secure communication. Phys. Lett. A 305, 365–370 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pikovsky, A.S., Rosenblum, M.G., Osipov, G.V., Kurths, J.: Phase synchronization of chaotic oscillators by external driving. Physica D 104, 219–238 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pikovsky, A.S., Zaks, M., Rosenblum, M., Osipov, G., Kurths, J.: Phase synchronization of chaotic oscillations in terms of periodic orbits. Chaos 7, 680–688 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhou, C.S., Kurths, J.: Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Phys. Rev. Lett. 88, 230602 (2002)

    Article  Google Scholar 

  17. Katriel, G.: Synchronization of oscillators coupled through an environment. Physica D 237, 2933–2944 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Resmi, V., Ambika, G., Amritkar, R.E.: Synchronized states in chaotic systems coupled indirectly through dynamic environment (2010). arXiv:0910.2382v2 [nlin.CD]

  19. Garcia-Ojalvo, J., Elowitz, M.B., Strogatz, S.H.: Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. Proc. Natl. Acad. Sci. USA 101, 10955–10960 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Danino, T., Mondragón-Palomino, O., Tsimring, L., Hasty, J.: A synchronized quorum of genetic clocks. Nature 463, 326–330 (2010)

    Article  Google Scholar 

  21. Misra, J.C., Mitra, A.: Synchronization among tumor-like cell aggregations coupled by quorum sensing: a theoretical study. Comput. Math. Appl. 55, 1842–1853 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. McMillen, D., Kopell, N., Hasty, J., Collins, J.J.: Synchronizing genetic relaxation oscillators by intercell signaling. Proc. Natl. Acad. Sci. USA 99, 679–684 (2002)

    Article  Google Scholar 

  23. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  24. Leloup, J.C., Goldbeter, A.: A model for circadian rhythms in drosophila incorporating the formation of a complex between the PER and TIM proteins. J. Biol. Rhythms 13, 70–87 (1998)

    Article  Google Scholar 

  25. Glossop, N.R., Lyons, L.C., Hardin, P.E.: Interlocked feedback loops within the drosophila circadian oscillator. Science 286, 766–768 (1999)

    Article  Google Scholar 

  26. Chialvo, D.R., Gilmour, J., Jalife, J.: Low dimensional chaos in cardiac tissue. Nature 343, 653–657 (1990)

    Article  Google Scholar 

  27. Courtemanche, M., Glass, L., Rosengarten, M.D., Goldberger, A.L.: Beyond pure parasystole: promises and problems in modeling complex arrhythmias. Am. J. Physiol. 257, H693–H706 (1989)

    Google Scholar 

  28. Chen, A.: Modeling a synthetic biological chaotic system: relaxation oscillators coupled by quorum sensing. Nonlinear Dyn. 63, 711–718 (2011)

    Article  Google Scholar 

  29. Guo, L., Zhenyuan, X.: Adaptive coupled synchronization of non-autonomous systems in ring networks. Chin. Phys. B. 17, 836–841 (2008)

    Article  MATH  Google Scholar 

  30. Li, J., Zhao, X., Liu, Z.: Generalized Hamilton Systems Theory and Its Applications. Science, Beijing (1997)

    Google Scholar 

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Acknowledgements

The paper is supported by the National Science Foundation of PR China under Grants No 11002061, 11202084, 10901073 and “the Fundamental Research Funds for the Central Universities”.

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Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, China

    Liuxiao Guo, Manfeng Hu, Zhenyuan Xu & Aihua Hu

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  1. Liuxiao Guo
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  2. Manfeng Hu
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  3. Zhenyuan Xu
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  4. Aihua Hu
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Correspondence to Liuxiao Guo.

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Guo, L., Hu, M., Xu, Z. et al. Synchronization and chaos control by quorum sensing mechanism. Nonlinear Dyn 73, 1253–1269 (2013). https://doi.org/10.1007/s11071-013-0769-z

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  • DOI: https://doi.org/10.1007/s11071-013-0769-z

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