Restoration of rhythmicity in diffusively coupled dynamical networks

Wei Zou (), D. V. Senthilkumar, Raphael Nagao, István Z. Kiss (), Yang Tang, Aneta Koseska, Jinqiao Duan and Jürgen Kurths
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Wei Zou: School of Mathematics and Statistics, Huazhong University of Science and Technology
D. V. Senthilkumar: Potsdam Institute for Climate Impact Research, Telegraphenberg
Raphael Nagao: Saint Louis University
István Z. Kiss: Saint Louis University
Yang Tang: Potsdam Institute for Climate Impact Research, Telegraphenberg
Aneta Koseska: Max Planck Institute of Molecular Physiology
Jinqiao Duan: School of Mathematics and Statistics, Huazhong University of Science and Technology
Jürgen Kurths: Potsdam Institute for Climate Impact Research, Telegraphenberg

Nature Communications, 2015, vol. 6, issue 1, 1-9

Abstract: 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.

Date: 2015
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DOI: 10.1038/ncomms8709

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