Eur. Phys. J. Special Topics 229, 729–741 (2020)
https://doi.org/10.1140/epjst/e2020-900202-5

Regular Article

Behaviors of solutions to network diffusion equation with power-nonlinearity

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

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

^a e-mail: ohara@fuee.u-fukui.ac.jp

Received: 20 September 2019
Received in final form: 18 November 2019
Published online: 12 March 2020

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.