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

doi:10.1038/ncomms8709

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 journal › Article › peer-review

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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 language	English
Article number	7709
Number of pages	9
Journal	Nature Communications
Volume	6
Early online date	15 Jul 2015
DOIs	https://doi.org/10.1038/ncomms8709
Publication status	Published - Jul 2015

Bibliographical 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).

Keywords

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

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Restoration of rhythmicity in diffusively coupled dynamical networks
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Cite this

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title = "Restoration of rhythmicity in diffusively coupled dynamical networks",

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.",

keywords = "limit-cycle oscillators, delay-induced death, amplitude death, chemical oscillations, differential equations, electrical synapses, systems, synchronization, populations, states",

author = "Wei Zou and Senthilkumar, {D. V.} and Raphael Nagao and Kiss, {Istvan Z.} and Yang Tang and Aneta Koseska and Jinqiao Duan and Juergen Kurths",

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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AU - Zou, Wei

AU - Senthilkumar, D. V.

AU - Nagao, Raphael

AU - Kiss, Istvan Z.

AU - Tang, Yang

AU - Koseska, Aneta

AU - Duan, Jinqiao

AU - Kurths, Juergen

N1 - 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).

PY - 2015/7

Y1 - 2015/7

N2 - 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.

AB - 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.

KW - limit-cycle oscillators

KW - delay-induced death

KW - amplitude death

KW - chemical oscillations

KW - differential equations

KW - electrical synapses

KW - systems

KW - synchronization

KW - populations

KW - states

U2 - 10.1038/ncomms8709

DO - 10.1038/ncomms8709

M3 - Article

SN - 2041-1723

VL - 6

JO - Nature Communications

JF - Nature Communications

M1 - 7709

ER -

Restoration of rhythmicity in diffusively coupled dynamical networks

Abstract

Bibliographical note

Keywords

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