Pattern selection in the 2D FitzHugh–Nagumo model

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)535-549
Number of pages15
JournalRicerche di Matematica
Publication statusPublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Pattern selection in the 2D FitzHugh–Nagumo model'. Together they form a unique fingerprint.

Cite this