Impulse patterning and relaxation propagation in excitable media

C. Elphick, E. Meron, J. Rinzel, E. A. Spiegel

Research output: Contribution to journalArticlepeer-review


Wavetrains of impulses in homogeneous excitable media relax during propagation toward constant-speed patterns. Here we present a study of this relaxation process. Starting with the basic reaction-diffusion or cable equations, we derive kinematics for the trajectories of widely spaced impulses in the form of ordinary differential equations for the set of times at which impulses arrive at a given point in space. Stability criteria derived from these equations allow us to determine the possible asymptotic forms of propagating trains. When the recovery after excitation is monotonic, only one stable train exists for a given propagation speed. In the case of an oscillatory recovery, however, many stable trains are possible. This essential difference between monotonic and oscillatory recoveries manifests itself in qualitatively distinct relaxational behaviors.

Original languageEnglish (US)
Pages (from-to)249-268
Number of pages20
JournalJournal of Theoretical Biology
Issue number2
StatePublished - Sep 21 1990

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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