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Dynamical robustness in a heterogeneous network of globally coupled nonlinear oscillators

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  • Gowthaman, I.
  • Singh, Uday
  • Chandrasekar, V.K.
  • Senthilkumar, D.V.

Abstract

Deterioration or failure of even a fraction of the microscopic constituents of a large class of networks leads to the loss of the macroscopic activity of the network as a whole. We deduce the evolution equation of two macroscopic order parameters from a globally coupled network of heterogeneous oscillators following the self-consistent field approach under the strong coupling limit. The macroscopic order parameter is used to classify the stable nontrivial steady state and the macroscopic oscillatory state of the network. We examine the dynamical robustness of the network by including a limiting factor that limits the degree of diffusion and a self-feedback factor in the network in addition to the heterogeneity of the network. The heterogeneity is introduced using the parameter specifying the distance from the Hopf bifurcation, which is drawn from a random statistical distribution. We also deduce the critical stability curves from the evolution equation of the macroscopic order parameters demarcating the stable nontrivial steady state and the macroscopic oscillatory state in the system parameter space. We show that a large heterogeneity and a large self-feedback factor facilitates the onset of the stable macroscopic oscillatory state by destabilizing the aging transition state, whereas limiting the degree of the diffusion favors the sustained macroscopic oscillation of the heterogeneous network.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s096007792030789x
    DOI: 10.1016/j.chaos.2020.110396
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    References listed on IDEAS

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    1. Brey, J.J. & Casado, J.M. & Morillo, M., 1984. "On the dynamics of a stochastic nonlinear mean-field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 497-508.
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    3. Luca Ambrogioni & Marcel A J van Gerven & Eric Maris, 2017. "Dynamic decomposition of spatiotemporal neural signals," PLOS Computational Biology, Public Library of Science, vol. 13(5), pages 1-37, May.
    4. 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.
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    Cited by:

    1. Wang, Yuexin & Sun, Zhongkui & Zhang, Hanqi & Zhou, Yining & Liu, Shutong & Xu, Wei, 2024. "Dynamic survivability of two-layer networks: The role of interlayer coupling," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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