Are buffers boring? Uniqueness and asymptotical stability of traveling wave fronts in the buffered bistable system

Je Chiang Tsai, James Sneyd

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Traveling waves of calcium are widely observed under the condition that the free cytosolic calcium is buffered. Thus it is of physiological interest to determine how buffers affect the properties of calcium waves. Here we summarise and extend previous results on the existence, uniqueness and stability of traveling wave solutions of the buffered bistable equation, which is the simplest possible model of the upstroke of a calcium wave. Taken together, the results show that immobile buffers do not change the existence, uniqueness or stability of the traveling wave, while mobile buffers can eliminate a traveling wave. However, if a wave exists in the latter case, it remains unique and stable.

Original languageEnglish
Pages (from-to)513-553
Number of pages41
JournalJournal of Mathematical Biology
Volume54
Issue number4
DOIs
Publication statusPublished - 2007 Apr 1

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Keywords

  • Bistable equation
  • Calcium
  • FitzHugh-Nagumo equations
  • Reaction-diffusion equations
  • Stability
  • Traveling wave

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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