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Distinct collective states due to trade-off between attractive and repulsive couplings

K. Sathiyadevi1, V. K. Chandrasekar1,*, D. V. Senthilkumar2,*, and M. Lakshmanan3

  • 1Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
  • 2School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, India
  • 3Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India

  • *Corresponding authors:
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Phys. Rev. E 97, 032207 – Published 19 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032207

Abstract

We investigate the effect of repulsive coupling together with an attractive coupling in a network of nonlocally coupled oscillators. To understand the complex interaction between these two couplings we introduce a control parameter in the repulsive coupling which plays a crucial role in inducing distinct complex collective patterns. In particular, we show the emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling. In the oscillatory cluster state, the oscillators in the network are grouped into two distinct dynamical states of homogeneous and inhomogeneous oscillatory states. Further, the network of coupled oscillators follow the same transition route in the entire coupling range. Depending upon distinct coupling ranges, the system displays different number of clusters in the death state and oscillatory state. We also observe that the number of coherent domains in the oscillatory cluster state exponentially decreases with increase in coupling range and obeys a power-law decay. Additionally, we show analytical stability for observed solitary state, synchronized state, and incoherent oscillation death state.

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References (55)

  1. A. Pikovsky, M. G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
  2. W. Zou, D. V. Senthilkumar, R. Nagao, I. Z. Kiss, Y. Tang, A. Koseska, J. Duan, and J. Kurths, Nat. Commun. 6, 7709 (2015)
  3. D. G. Aronson, G. B. Ermentrout, and N. Koppel, Physica D 41, 403 (1990).
  4. P. C. Matthews and S. H. Strogatz, Phys. Rev. Lett. 65, 1701 (1990); P. C. Matthews, R. E. Mirollo, and S. H. Strogatz, Physica D 52, 293 (1991).
  5. A. Sharma and M. D. Shrimali, Phys. Rev. E 85, 057204 (2012).
  6. A. Koseska, E. I. Volkov, A. Zaikin, and J. Kurths, Phys. Rev. E 75, 031916 (2007).
  7. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 80, 5109 (1998).
  8. I. Prigogine and R. Lefever, J. Chem. Phys. 48, 1695 (1968); A. Koseska, E. Volkov, and Kurths, J. Phys. Rep. 531, 173 (2013).
  9. W. Zou, D. V. Senthilkumar, Y. Tang, and J. Kurths, Phys. Rev. E 86, 036210 (2012).
  10. W. Zou, D. V. Senthilkumar, J. Duan, and J. Kurths, Phys. Rev. E 90, 032906 (2014).
  11. K. Konishi, Phys. Rev. E 68, 067202 (2003).
  12. R. Karnatak, R. Ramaswamy, and A. Prasad, Phys. Rev. E 76, 035201(R) (2007).
  13. V. Resmi, G. Ambika, and R. E. Amritkar, Phys. Rev. E 84, 046212 (2011).
  14. C. R. Hens, O. I. Olusola, P. Pal, and S. K. Dana, Phys. Rev. E 88, 034902 (2013).
  15. E. Ullner, A. Zaikin, E. I. Volkov, and J. Garcia-Ojalvo, Phys. Rev. Lett. 99, 148103 (2007).
  16. M. F. Crowley and I. R. Epstein, J. Phys. Chem. 93, 2496 (1989).
  17. M. Toiya, V. K. Vanag, and I. R. Epstein, Angew. Chem., Int. Ed. 47, 7753 (2008).
  18. K. P. Zeyer, M. Mangold, and E. D. Gilles, J. Phys. Chem. A 105, 7216 (2001).
  19. M. Heinrich, T. Dahms, V. Flunkert, S. W. Teitsworth, and E. Schöll, New J. Phys. 12, 113030 (2010).
  20. A. Mishra, S. Saha, P. K. Roy, T. Kapitaniak, and S. K. Dana, Chaos 27, 023110 (2017).
  21. Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002).
  22. D. M. Abrams and S. H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004).
  23. D. M. Abrams and S. H. Strogatz, Int. J. Bif. Choas 16, 21 (2006).
  24. M. J. Panaggio and D. M. Abrams, Nonlinearity 28, R67 (2015).
  25. I. Omelchenko, A. Provata, J. Hizanidis, E. Schöll, and P. Hövel, Phys. Rev. E 91, 022917 (2015).
  26. T. Banerjee, P. S. Dutta, A. Zakharova, and E. Schöll, Phys. Rev. E 94, 032206 (2016).
  27. I. Omelchenko, Y. Maistrenko, P. Hövel, and E. Schöll, Phys. Rev. Lett. 106, 234102 (2011).
  28. V. Semenov, A. Feoktistov, T. Vadivasova, E. Schöll, and A. Zakharova, Chaos 25, 033111 (2015).
  29. R. Gopal, V. K. Chandrasekar, A Venkatesan, and M Lakshmanan, Phys. Rev. E 89, 052914 (2014).
  30. K. Kaneko, Physica D 41, 137 (1990); Chaos 25, 097608 (2015); A. Yeldesbay, A. Pikovsky, and M. Rosenblum, Phys. Rev. Lett. 112, 144103 (2014); G. C. Sethia and A. Sen, ibid. 112, 144101 (2014).
  31. V. K. Chandrasekar, R. Gopal, A. Venkatesan, and M. Lakshmanan, Phys. Rev. E 90, 062913 (2014).
  32. A. Mishra, C. Hens, M. Bose, P. K. Roy, and S. K. Dana, Phys. Rev. E 92, 062920 (2015).
  33. B. K. Bera, D. Ghosh, and M. Lakshmanan, Phys. Rev. E 93, 012205 (2016).
  34. C. R. Laing, Phys. Rev. E 92, 050904(R) (2015).
  35. B. K. Bera and D. Ghosh, Phys. Rev. E 93, 052223 (2016).
  36. B. K. Bera, D. Ghosh, and T. Banerjee, Phys. Rev. E 94, 012215 (2016).
  37. N. C. Rattenborg, C. J. Amlaner, and S.L. Lima, Neurosci. Biobehav. Rev. 2, 817 (2000).
  38. A. Rothkegel and K. Lehnertz, New J. Phys. 16, 055006 (2014).
  39. C. R. Laing and C. C. Chow, Neural Comput. 13, 1473 (2001).
  40. H. Sakaguchi, Phys. Rev. E 73, 031907 (2006).
  41. A. E. Filatova, A. E. Hramov, A. A. Koronovskii, and S. Boccaletti, Chaos 18, 023133 (2008).
  42. J. C. Gonz alez-Avella, M. G. Cosenza, and M. San Miguel, Physica A 399, 24 (2014).
  43. A. Zakharova, M. Kapeller, and E. Schöll, Phys. Rev. Lett. 112, 154101 (2014).
  44. A. Zakharova, M. Kapeller, and E. Schöll, IOP Publishing, Conference Series 727, 012018 (2016).
  45. L. Tumash, A. Zakharova, J. Lehnert, W. Just, and E. Schöll, Europhys. Lett. 117, 20001 (2017).
  46. K. Premalatha, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Phys. Rev. E 93, 052213 (2016).
  47. K. Premalatha, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Phys. Rev. E 91, 052915 (2015).
  48. Z. Qu, Y. Shiferaw, and J. N. Weiss, Phys. Rev. E 75, 011927 (2007).
  49. T. Yanagita, T. Ichinomiya, and Y. Oyama, Phys. Rev. E 72, 056218 (2005).
  50. Xiao-Jun Tian, Xiao-Peng Zhang, F. Liu, and W. Wang, Phys. Rev. E 80, 011926 (2009)
  51. J. Guckenheimer, K. Hoffman, and W. Weckesser, Numerical computation of canards, Int. J. Bifurcat. Chaos Appl. Sci. Eng. 10, 2669 (2000).
  52. P. F. Rowat and A. I. Selverston, Modeling the gastric mill central pattern generator of the lobsterwith a relaxation-oscillator network, J. Neurophysiol. 70, 1030 (1993).
  53. H. Daido and K. Nakanishi, Phys. Rev. Lett. 96, 054101 (2006).
  54. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
  55. V. K. Chandrasekar, R. Gopal, D. V. Senthilkumar, and M. Lakshmanan, Phys. Rev. E 94, 012208 (2016).

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Phys. Rev. E 97, 032207– Published 19 March, 2018
  • Received 4 January 2018
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