Ricerche di Matematica

, Volume 68, Issue 2, pp 535–549 | Cite as

Pattern selection in the 2D FitzHugh–Nagumo model

  • G. GambinoEmail author
  • M. C. Lombardo
  • G. Rubino
  • M. Sammartino


We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.


FitzHugh–Nagumo model Turing instability Square patterns Amplitude equations 

Mathematics Subject Classification

37L10 70K50 35B36 



The results contained in the present paper have been partially presented in Wascom 2017. The work of GG and GR was partially supported by GNFM-INdAM through a Progetto Giovani grant. The work of MCL and MS was partially supported by GNFM-INdAM.


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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  • G. Gambino
    • 1
    Email author
  • M. C. Lombardo
    • 1
  • G. Rubino
    • 1
  • M. Sammartino
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly
  2. 2.DIIDUniversity of PalermoPalermoItaly

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