Waves in a simple, excitable or oscillatory, reaction-diffusion model

G. Bard Ermentrout, John Rinzel

Research output: Contribution to journalArticle

Abstract

A simple one variable caricature for oscillating and excitable reaction-diffusion systems is introduced. It is shown that as a parameter, λ, varies the system dynamics change from oscillatory (λ > λ<inf>0</inf>) to excitable (λ < λ<inf>0</inf>) and the frequency of the oscillation vanishes as {Mathematical expression} for λ ↘ λ<inf>0</inf>. When such dynamics are coupled by continuous diffusion in a ring geometry (1-space dimension), propagating wave trains may be found. On an infinite ring excitable devices lead to unique solitary waves which are analogous to "pulse" waves. A solvable example is presented, illustrating properties of dispersion, excitability, and waves. Finally it is shown that the caricature arises in a natural way from more general excitable/oscillatory systems.

Original languageEnglish (US)
Pages (from-to)269-294
Number of pages26
JournalJournal of Mathematical Biology
Volume11
Issue number3
DOIs
StatePublished - 1981

Fingerprint

Caricatures
Reaction-diffusion Model
Excitable Systems
Ring
oscillation
Excitability
Solitary Waves
Solitons
Reaction-diffusion System
System Dynamics
Equipment and Supplies
Vanish
Dynamical systems
Vary
Oscillation
Geometry

Keywords

  • Excitability
  • Oscillation
  • Pulse waves
  • Rings
  • Waves

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Waves in a simple, excitable or oscillatory, reaction-diffusion model. / Bard Ermentrout, G.; Rinzel, John.

In: Journal of Mathematical Biology, Vol. 11, No. 3, 1981, p. 269-294.

Research output: Contribution to journalArticle

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