Bifurcations of canard-induced mixed mode oscillations in a pituitary lactotroph model

Theodore Vo, Richard Bertram, Martin Wechselberger

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16 Citations (Scopus)

Abstract

Mixed mode oscillations (MMOs) arc complex oscillatory waveforms that naturally occur in physiologically relevant dynamical processes. MMOs were studied in a model of electrical bursting in a pituitary lactotroph [34] where geometric singular perturbation theory and bifurcation analysis were combined to demonstrate that the MMOs arise from canard dynamics. In this work, we extend the analysis done in [34] and consider bifurcations of canard solutions under variations of key parameters. To do this, a global return map induced by the flow of the equations is constructed and a qualitative analysis given. The canard solutions act as separatrices in the return maps, organising the dynamics along the Poincaré section. We examine the bifurcations of the return maps and demonstrate that the map formulation allows for an explanation of the different MMO patterns observed in the lactotroph model.

Original languageEnglish
Pages (from-to)2879-2912
Number of pages34
JournalDiscrete and Continuous Dynamical Systems Series A
Volume32
Issue number8
DOIs
Publication statusPublished - 1 Aug 2012
Externally publishedYes

Keywords

  • Bifurcations
  • Canards
  • Geometric singular perturbation theory
  • MMOs
  • Return maps

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