Nonlinear Dynamics

, Volume 91, Issue 4, pp 2219–2225 | Cite as

Revival of oscillations via common environment

  • Manish Yadav
  • Amit Sharma
  • Manish Dev ShrimaliEmail author
  • Sudeshna Sinha
Original Paper


We explore the behavior of groups of Landau-Stuart oscillators, with diffusive mean-field coupling within the group and indirect inter-group coupling mediated by a common medium. Interestingly, we find that oscillations are revived in groups with fixed point dynamics by coupling to an oscillatory group through the common medium. We also investigate groups of Hindmarsh–Rose model neurons and demonstrate the emergence of spiking in indirectly coupled inactive neuronal groups, indicating the vital role of the common medium in restoring oscillations.


Revival of oscillations Mean-field coupling Network Common environment 



We acknowledge the support from DST, New Delhi.


  1. 1.
    Sharma, A., Shrimali, M.D.: Amplitude death with mean-field diffusion. Phys. Rev. E 85, 057204 (2012)CrossRefGoogle Scholar
  2. 2.
    Prasad, A., Dhamala, M., Adhikari, B.M., Ramaswamy, R.: Amplitude death in nonlinear oscillators with nonlinear coupling. Phys. Rev. E 81, 027201 (2010)CrossRefGoogle Scholar
  3. 3.
    Banerjee, T., Ghosh, D.: Transition from amplitude to oscillation death under mean-field diffusive coupling. Phys. Rev. E 89, 052912 (2014)CrossRefGoogle Scholar
  4. 4.
    Kamal, N.K., Sharma, P.R., Shrimali, M.D.: Oscillation suppression in indirectly coupled limit cycle oscillators. Phys. Rev. E 92, 022928 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Sharma, A., Sharma, P.R., Shrimali, M.D.: Amplitude death in nonlinear oscillators with indirect coupling. Phys. Lett. A 376, 1562 (2012)CrossRefzbMATHGoogle Scholar
  6. 6.
    Karnatak, R., Ramaswamy, R., Feudel, U.: Conjugate coupling in ecosystems: cross-predation stabilizes food webs. Chaos Solitons Fractals 68, 48 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kiss, I.Z., Hudson, J.L.: Phase synchronization and suppression of chaos through intermittency in forcing of an electrochemical oscillator. Phys. Rev. E 64, 046215 (2001)CrossRefGoogle Scholar
  8. 8.
    Ermentrout, G.B., Kopell, N.: Oscillator death in systems of coupled neural oscillators. SIAM J. Appl. Math. 50, 125 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Gallego, B., Cessi, P.: Decadal variability of two oceans and an atmosphere. J. Clim. 14, 2815 (2001)CrossRefGoogle Scholar
  10. 10.
    Prasad, A.: Amplitude death in coupled chaotic oscillators. Phys. Rev. E 72, 056204 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zou, W., Senthilkumar, D., Nagao, R., Kiss, I.Z., Tang, Y., Koseska, A., Duan, J., Kurths, J.: Restoration of rhythmicity in diffusively coupled dynamical networks. Nat. Commun. 6, 7709 (2015)CrossRefGoogle Scholar
  12. 12.
    Zou, W., Senthilkumar, D., Zhan, M., Kurths, J.: Reviving oscillations in coupled nonlinear oscillators. Phys. Rev. Lett. 111, 014101 (2013)CrossRefGoogle Scholar
  13. 13.
    Ghosh, D., Banerjee, T., Kurths, J.: Revival of oscillation from mean-field-induced death: theory and experiment. Phys. Rev. E 92, 052908 (2015)CrossRefGoogle Scholar
  14. 14.
    Zou, W., Yao, C., Zhan, M.: Eliminating delay-induced oscillation death by gradient coupling. Phys. Rev. E 82, 056203 (2010)CrossRefGoogle Scholar
  15. 15.
    Kar, S., Ray, D.S.: Collapse and revival of glycolytic oscillation. Phys. Rev. Lett. 90, 238102 (2003)CrossRefGoogle Scholar
  16. 16.
    Cao, H., Huang, R.K., Yamamoto, Y., Jiang, S., Machida, S., Takiguchi, Y.: Collapse and revival of the oscillation of microcavity emission and its phase spectrum. Phys. Stat. Solidi 164, 29 (1997)CrossRefGoogle Scholar
  17. 17.
    Sneyd, J., Tsaneva-Atanasova, K., Yule, D.I., Thompson, J.L., Shuttleworthi, T.J.: Control of calcium oscillations by membrane fluxes. Proc. Natl. Acad. Sci. USA 101, 1392 (2004)CrossRefGoogle Scholar
  18. 18.
    Brgers, C., Epstein, S., Kopell, N.J.: Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model. Proc. Natl. Acad. Sci. USA 105, 18023 (2008)CrossRefGoogle Scholar
  19. 19.
    Sawai, S., Maeda, Y., Sawada, Y.: Spontaneous symmetry breaking turing-type pattern formation in a confined Dictyostelium cell mass. Phys. Rev. Lett. 85, 2212–2215 (2000)CrossRefGoogle Scholar
  20. 20.
    Toth, R., Taylor, A.F., Tinsley, M.R.: Collective behavior of a population of chemically coupled oscillators. J. Phys. Chem. B 110, 10170–10176 (2006)CrossRefGoogle Scholar
  21. 21.
    Kondo, S., Miura, T.: Reaction–diffusion model as a framework for understanding biological pattern formation. Science 329, 1616–1620 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Richard, P., Bakker, B.M., Teusink, B., Dam, K.V., Westerhoff, H.V.: Acetaldehyde mediates the synchronization of sustained glycolytic oscillations in populations of yeast cells. Eur. J. Biochem. 235, 238 (1996)CrossRefGoogle Scholar
  23. 23.
    Shockley, K., Butwill, M., Zbilut Jr., J.P., Webber, C.L.: Cross recurrence quantification of coupled oscillators. Phys. Lett. A 305, 59 (2002)CrossRefzbMATHGoogle Scholar
  24. 24.
    Resmi, V., Ambika, G., Amritkar, R.E.: Synchronized states in chaotic systems coupled indirectly through a dynamic environment. Phys. Rev. E 81, 046216 (2010)CrossRefGoogle Scholar
  25. 25.
    Majhi, S., Bera, B.K., Bhowmick, S.K., Ghosh, D.: Restoration of oscillation in network of oscillators in presence of direct and indirect interactions. Phys. Lett. A 380, 3617 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Hindmarsh, J.L., Rose, R.M.: A model of neuronal bursting using three coupled first order differential equations. Proc. R. Soc. Lond. Ser. B 221, 87 (1984)CrossRefGoogle Scholar
  27. 27.
    Mamat, M., Kueniawan, P.W., Kartono, A., Salleh, Z.: Mathematical model of dynamics and synchronization of coupled neurons using Hindmarsh–Rose model. Appl. Math. Sci. 6, 2489 (2012)zbMATHGoogle Scholar
  28. 28.
    Checco, P., Biey, M., Righero, M., Kocarev, L.: Synchronization and bifurcations in networks of coupled Hindmarsh–Rose neurons. In: IEEE International Symposium on Circuits and Systems, New Orleans, LA, pp. 1541–1544 (2007)Google Scholar
  29. 29.
    Perin, R., Berger, T.K., Markram, H.: A synaptic organizing principle for cortical neuronal groups. Proc. Natl. Acad. Sci. USA 108, 5419 (2011)CrossRefGoogle Scholar
  30. 30.
    Litwin-Kumar, A., Doiron, B.: Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat. Neurosci. 15, 1498 (2012)CrossRefGoogle Scholar
  31. 31.
    Rosenblum, M., Pikovsky, A.: Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators. Contemp. Phys. 44, 401–416 (2003)CrossRefGoogle Scholar
  32. 32.
    Banghart, M., Borges, K., Isacoff, E., Trauner, D., Kramer, R.H.: Light-activated ion channels for remote control of neuronal firing. Nat. Neurosci. 7, 1381 (2004)CrossRefGoogle Scholar
  33. 33.
    Steinlein, O.K., Noebels, J.L.: Ion channels and epilepsy in man and mouse. Curr. Opin. Genet. Dev. 10, 286 (2000)CrossRefGoogle Scholar
  34. 34.
    Kagana, B.L., Hirakura, Y., Azimov, R., Azimova, R., Lin, M.C.: The channel hypothesis of Alzheimer’s disease: current status. Pepetides 23, 1311 (2002)CrossRefGoogle Scholar
  35. 35.
    Ozer, M., Perc, M., Uzuntarla, M.: Controlling the spontaneous spiking regularity via channel blocking on Newman-Watts networks of Hodgkin–Huxley neurons. Europhys. Lett. 86, 40008 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Manish Yadav
    • 1
  • Amit Sharma
    • 2
  • Manish Dev Shrimali
    • 2
    Email author
  • Sudeshna Sinha
    • 1
  1. 1.Indian Institute of Science Education and Research MohaliMohaliIndia
  2. 2.Department of PhysicsCentral University of RajasthanAjmerIndia

Personalised recommendations