Restoration of rhythmicity in diffusively coupled dynamical networks

Wei Zou*, D. V. Senthilkumar, Raphael Nagao, Istvan Z. Kiss, Yang Tang, Aneta Koseska, Jinqiao Duan, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticle

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Abstract

Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in) homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.

Original languageEnglish
Article number7709
Number of pages9
JournalNature Communications
Volume6
Early online date15 Jul 2015
DOIs
Publication statusPublished - Jul 2015

Keywords

  • limit-cycle oscillators
  • delay-induced death
  • amplitude death
  • chemical oscillations
  • differential equations
  • electrical synapses
  • systems
  • synchronization
  • populations
  • states

Cite this

Zou, W., Senthilkumar, D. V., Nagao, R., Kiss, I. Z., Tang, Y., Koseska, A., ... Kurths, J. (2015). Restoration of rhythmicity in diffusively coupled dynamical networks. Nature Communications, 6, [7709]. https://doi.org/10.1038/ncomms8709

Restoration of rhythmicity in diffusively coupled dynamical networks. / Zou, Wei; Senthilkumar, D. V.; Nagao, Raphael; Kiss, Istvan Z.; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Juergen.

In: Nature Communications, Vol. 6, 7709, 07.2015.

Research output: Contribution to journalArticle

Zou, W, Senthilkumar, DV, Nagao, R, Kiss, IZ, Tang, Y, Koseska, A, Duan, J & Kurths, J 2015, 'Restoration of rhythmicity in diffusively coupled dynamical networks', Nature Communications, vol. 6, 7709. https://doi.org/10.1038/ncomms8709
Zou W, Senthilkumar DV, Nagao R, Kiss IZ, Tang Y, Koseska A et al. Restoration of rhythmicity in diffusively coupled dynamical networks. Nature Communications. 2015 Jul;6. 7709. https://doi.org/10.1038/ncomms8709
Zou, Wei ; Senthilkumar, D. V. ; Nagao, Raphael ; Kiss, Istvan Z. ; Tang, Yang ; Koseska, Aneta ; Duan, Jinqiao ; Kurths, Juergen. / Restoration of rhythmicity in diffusively coupled dynamical networks. In: Nature Communications. 2015 ; Vol. 6.
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abstract = "Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in) homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.",
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note = "We acknowledge financial support from the National Natural Science Foundation of China (No. 11202082, No. 61203235, No. 11371367 and No. 11271290), the Fundamental Research Funds for the Central Universities of China under Grant No. 2014QT005, IRTG1740(DFG-FAPESP), and SERB-DST Fast Track scheme for young scientist under Grant No. ST/FTP/PS-119/2013, NSF CHE-0955555 and Grant No. 229171/2013-3 (CNPq).",
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