Properties of a bursting model with two slow inhibitory variables

Paul Smolen, David Terman, John Rinzel

Research output: Contribution to journalArticlepeer-review


Models for certain excitable cells, such as the pancreatic B-cell, must reproduce ″bursting″ oscillations of the membrane potential. This has previously been done using one slow variable to drive bursts. The dynamics of such models have been analyzed. However, new models for the B-cell often include additional slow variables, and therefore the previous analysis is extended to two slow variables, using a simplified version of a B-cell model. Some unusual time courses of this model motivated a geometric singular perturbation analysis and the application of averaging to reduce the dynamics to the slow-variable phase plane. A geometric understanding of the solution structure and of transitions between various modes of behavior was then developed.

Original languageEnglish (US)
Pages (from-to)861-892
Number of pages32
JournalSIAM Journal on Applied Mathematics
Issue number3
StatePublished - 1993

ASJC Scopus subject areas

  • Applied Mathematics


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