Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion

E.P. Zemskov, I.R. Epstein, A. Muntean

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)


We study FitzHugh–Nagumo type reaction–diffusion systems with linear cross-diffusion terms. Based on an analytical description using piecewise linear approximations of the reaction functions, we completely describe the occurrence and properties of wavy pulses, patterns of relevance in several biological contexts, in two prototypical systems. The pulse wave profiles arising in this treatment contain oscillatory tails similar to those in travelling fronts. We find a fundamental, intrinsic feature of pulse dynamics in cross-diffusive systems—the appearance of pulses in the bistable regime when two fixed points exist.
Original languageEnglish
Pages (from-to)217-226
JournalMathematical Medicine and Biology
Publication statusPublished - 2011


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