title: Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion.
abstract: 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.
authors.affiliation: Department of Chemistry, Brandeis University, MS 015, Waltham, MA 02454, USA. zemskov@brandeis.edu
authors.forename: E P
authors.initials: EP
authors.lastname: Zemskov
authors.forename: I R
authors.initials: IR
authors.lastname: Epstein
authors.forename: A
authors.initials: A
authors.lastname: Muntean
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D007700:Kinetics; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted