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Restoration of rhythmicity in diffusively coupled dynamical networks

Author

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  • Wei Zou

    (School of Mathematics and Statistics, Huazhong University of Science and Technology
    Center for Mathematical Sciences, Huazhong University of Science and Technology
    Potsdam Institute for Climate Impact Research, Telegraphenberg)

  • D. V. Senthilkumar

    (Potsdam Institute for Climate Impact Research, Telegraphenberg
    Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University)

  • Raphael Nagao

    (Saint Louis University)

  • István Z. Kiss

    (Saint Louis University)

  • Yang Tang

    (Potsdam Institute for Climate Impact Research, Telegraphenberg
    The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology)

  • Aneta Koseska

    (Max Planck Institute of Molecular Physiology
    Research Centre for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts)

  • Jinqiao Duan

    (School of Mathematics and Statistics, Huazhong University of Science and Technology
    Center for Mathematical Sciences, Huazhong University of Science and Technology
    Illinois Institute of Technology)

  • Jürgen Kurths

    (Potsdam Institute for Climate Impact Research, Telegraphenberg
    Institute of Physics, Humboldt University Berlin
    Institute for Complex Systems and Mathematical Biology, University of Aberdeen
    Nizhny Novgorod State University)

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.

Suggested Citation

  • Wei Zou & D. V. Senthilkumar & Raphael Nagao & István Z. Kiss & Yang Tang & Aneta Koseska & Jinqiao Duan & Jürgen Kurths, 2015. "Restoration of rhythmicity in diffusively coupled dynamical networks," Nature Communications, Nature, vol. 6(1), pages 1-9, November.
    • Handle: RePEc:nat:natcom:v:6:y:2015:i:1:d:10.1038_ncomms8709
    DOI: 10.1038/ncomms8709
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    Cited by:

    1. Jianxi Gao & Xueming Liu & Daqing Li & Shlomo Havlin, 2015. "Recent Progress on the Resilience of Complex Networks," Energies, MDPI, vol. 8(10), pages 1-24, October.
    2. Sathiyadevi, K. & Premraj, D. & Banerjee, Tanmoy & Zheng, Zhigang & Lakshmanan, M., 2022. "Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Gowthaman, I. & Singh, Uday & Chandrasekar, V.K. & Senthilkumar, D.V., 2021. "Dynamical robustness in a heterogeneous network of globally coupled nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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