Turing patterns in a network-reduced FitzHugh-Nagumo model

Timoteo Carletti, Hiroya Nakao

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Reduction of a two-component FitzHugh-Nagumo model to a single-component model with long-range connection is considered on general networks. The reduced model describes a single chemical species reacting on the nodes and diffusing across the links with weighted long-range connections, which can be interpreted as a class of networked dynamical systems on a multigraph with local and nonlocal Laplace matrices that self-consistently emerge from the adiabatic elimination. We study the conditions for the instability of homogeneous states in the original and reduced models and show that Turing patterns can emerge in both models. We also consider generality of the adiabatic elimination for a wider class of slow-fast systems and discuss the peculiarity of the FitzHugh-Nagumo model.
Original languageEnglish
Article number022203
Number of pages12
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 13 Feb 2020


  • dynamics on networks
  • network diffusion
  • pattern formation


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