Pinned Solutions in a Heterogeneous Three-Component FitzHugh–Nagumo Model

  • Peter van Heijster
  • Chao-Nien Chen
  • Yasumasa Nishiura
  • Takashi Teramoto


We analyse pinned front and pulse solutions in a singularly perturbed three-component FitzHugh–Nagumo model with a small jump-type heterogeneity. We derive explicit conditions for the existence and stability of these type of pinned solutions by combining geometric singular perturbation techniques and an action functional approach. Most notably, in certain parameter regimes we can explicitly compute the pinning distance of a localised solution to the defect.


Reaction–diffusion equations Defects Calculus of variations Singular perturbations Existence Stability Localised defect solutions 

Mathematics Subject Classification

34A34 34A36 34C37 35B25 35B35 35K57 49J40 



PvH thanks the National Changhua University of Education in Taiwan, the National Center for Theoretical Sciences in Taiwan, and Tohoku University in Japan for their hospitality. CNC is grateful for the warm hospitality of Queensland University of Technology in Australia. YN and TT also thank Queensland University of Technology in Australia and the National Tsing-Hua University in Taiwan for their hospitality. The authors also acknowledge support from the Mathematics Research Promotion Center in Taiwan and they note that part of this research was finalised during the first joint Australia-Japan workshop on dynamical systems with applications in life sciences at Queensland University of Technology in Australia.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
  2. 2.Department of MathematicsNational Tsing Hua UniversityHsinchuTaiwan
  3. 3.WPI Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan
  4. 4.School of MedicineAsahikawa Medical UniversityAsahikawaJapan

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