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Unraveling the primary mechanisms leading to synchronization response in dissimilar oscillators

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Abstract

We study how the phenomenon of response to synchronization arises in sets of pulse-coupled dissimilar oscillators. One of the sets is constituted by oscillators that can easily synchronize. Conversely, the oscillators of the other set do not synchronize. When the elements of the first set are not synchronized, they induce oscillation death in the constituents of the second set. By contrast, when synchronization is achieved in oscillators of the first set, those of the second set recover their oscillatory behavior and thus, responding to synchronization. Additionally, we found another interesting phenomenon in this type of systems, namely, a new control of simultaneous firings in a population of similar oscillators attained by means of the action of a dissimilar oscillator.

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References

  1. I. Blekhman, Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications (World Scientific, Singapore, 2000)

  2. I.I. Blekhman, Synchronization in Science and Technology (ASME Press, New York, 1988)

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

  4. S. Boccaletti, L.M. Pecora, A. Pelaez, Phys. Rev. E 63, 066219 (2001)

    Article  ADS  Google Scholar 

  5. H. Nijmeije, A. Rodriguez-Angeles, Synchronization of Mechanical Systems (World Scientific, Singapore, 2003)

  6. A. Stefanski, Determining Thresholds of Complete Synchronization, and Application (World Scientific, 2009)

  7. H. Fukuda, H. Morimura, S. Kai, Physica D 205, 80 (2005)

    Article  ADS  Google Scholar 

  8. M. Lara-Aparicio, C. Barriga-Montoya, P. Padilla-Longoria, B. Fuentes-Pardo, Math. Biosci. Eng. 11, 317 (2014)

    MathSciNet  Google Scholar 

  9. J. Gonzalez-Miranda, Synchronization And Control Of Chaos: An Introduction For Scientists And Engineers (Imperial College Press, London, 2004)

  10. X.B. Lu, B.Z. Qin, Synchronization in Complex Networks (Nova Science, New York, 2011)

  11. A.E. Motter, S.A. Myers, M. Anghel, T. Nishikawa, Nat. Phys. 9, 191 (2013)

    Article  Google Scholar 

  12. G. Grinstein, R. Linsker, P. Natl. Acad. Sci. USA 102, 9948 (2005)

    Article  ADS  Google Scholar 

  13. W. Zhou, J. Yang, L. Zhou, D. Tong, Stability and Synchronization Control of Stochastic Neural Networks (Springer, Berlin, 2016)

  14. L. Kocarev, Consensus and Synchronization in Complex Networks (Springer, Berlin, 2013)

  15. R. Bader, Nonlinearities and Synchronization in Musical Acoustics and Music Psychology (Springer, Heidelberg, 2013)

  16. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  17. S.C. Manrubia, A.S. Mikhailov, D.H. Zanette, Emergence of Dynamical Order (World Scientific, Singapore, 2004)

  18. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  19. A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From Simple to Complex (Springer, Berlin, 2007)

  20. S. Boccaletti, The Synchronized Dynamics of Complex Systems (Elsevier, New York, 2008)

  21. J.A. Acebron, L.L. Bonilla, C.J.P. Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)

    Article  ADS  Google Scholar 

  22. F.A. Rodrigues, T.K.D.M. Peron, P. Ji, J. Kurths, Phys. Rep. 610, 1 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  23. Y. Kuramoto, Physica D 50, 15 (1991)

    Article  ADS  Google Scholar 

  24. S. Bottani, Phys. Rev. E 54, 2334 (1996)

    Article  ADS  Google Scholar 

  25. G.M. Ramírez Ávila, J. Kurths, J.L. Guisset, J.L. Deneubourg, Eur. Phys. J. Special Topics 223, 2759 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  27. W. Zou, D.V. Senthilkumar, J. Duan, J. Kurths, Phys. Rev. E 90, 032906 (2014)

    Article  ADS  Google Scholar 

  28. F.M. Atay, Physica D 183, 1 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  29. T. Banerjee, D. Biswas, Chaos 23, 043101 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  30. A. Koseska, E. Volkov, J. Kurths, Chaos 20, 023132 (2010)

    Article  ADS  Google Scholar 

  31. A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  32. A. Koseska, E. Volkov, J. Kurths, Phys. Rev. Lett. 111, 024103 (2013)

    Article  ADS  Google Scholar 

  33. J. Buck, E. Buck, Science 159, 1319 (1968)

    Article  ADS  Google Scholar 

  34. J. Copeland, A. Moiseff, J. Insect Physiol. 43, 965 (1997)

    Article  Google Scholar 

  35. A. Moiseff, J. Copeland, J. Insect Behav. 13, 597 (2000)

    Article  Google Scholar 

  36. N. Ohba, Integr. Comp. Biol. 44, 225 (2004)

    Article  Google Scholar 

  37. A.T. Winfree, J. Theor. Biol. 16, 15 (1967)

    Article  Google Scholar 

  38. R.E. Mirollo, S.H. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990)

    Article  MathSciNet  Google Scholar 

  39. G.M. Ramírez Ávila, J.L. Guisset, J.L. Deneubourg, Physica D 182, 254 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  40. J. Buck, J.F. Case, Biol. Bull. 121, 234 (1961)

    Article  Google Scholar 

  41. A. Moiseff, J. Copeland, Science 329, 181 (2010)

    Article  ADS  Google Scholar 

  42. G.M. Ramírez Ávila, J.L. Deneubourg, J.L. Guisset, N. Wessel, J. Kurths, Europhys. Lett. 94, 60007 (2011)

    Article  ADS  Google Scholar 

  43. T. Buschmann, A. Ewald, A. von Twickel, A. Bschges, Bioinspir. Biomim. 10, 041001 (2015)

    Article  ADS  Google Scholar 

  44. B.V.C. Martins, G. Brunetto, F. Sato, V.R. Coluci, D.S. Galvão, Chem. Phys. Lett. 453, 290 (2008)

    Article  ADS  Google Scholar 

  45. J. Buck, E. Buck, Am. Nat. 112, 471 (1978)

    Article  Google Scholar 

  46. W. Woods Jr, H. Hendrickson, J. Mason, S. Lewis, Am. Nat. 170, 702 (2007)

    Article  Google Scholar 

  47. E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge, 2007)

  48. P. Schultz, T. Peron, D. Eroglu, T. Stemler, G.M. Ramírez Ávila, F.A. Rodrigues, J. Kurths, Phys. Rev. E 93, 062211 (2016)

    Article  ADS  Google Scholar 

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Correspondence to Gonzalo Marcelo Ramírez-Ávila.

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Ramírez-Ávila, G.M., Kurths, J. Unraveling the primary mechanisms leading to synchronization response in dissimilar oscillators. Eur. Phys. J. Spec. Top. 225, 2487–2506 (2016). https://doi.org/10.1140/epjst/e2016-60033-5

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  • DOI: https://doi.org/10.1140/epjst/e2016-60033-5

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