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Behaviors of solutions to network diffusion equation with power-nonlinearity

A role of the q-exponential function for sufficiently large power-exponent

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Abstract

We study a certain class of network diffusion equation with large power-nonlinearity. We first report several interesting behaviors like synchronization and mode-switching, and next analytically clarify their mechanism. Throughout the investigation we demonstrate that the q-exponential function plays an important role and that the nonlinear behaviors are critically concerned with network topology.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui, 910-8507, Japan

    Xiaoyan Zhang, Taiga Senyo, Hiroto Sakai & Atsumi Ohara

Authors
  1. Xiaoyan Zhang
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  2. Taiga Senyo
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  3. Hiroto Sakai
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  4. Atsumi Ohara
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Correspondence to Atsumi Ohara.

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Zhang, X., Senyo, T., Sakai, H. et al. Behaviors of solutions to network diffusion equation with power-nonlinearity. Eur. Phys. J. Spec. Top. 229, 729–741 (2020). https://doi.org/10.1140/epjst/e2020-900202-5

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  • DOI: https://doi.org/10.1140/epjst/e2020-900202-5

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