Localized and asynchronous patterns via canards in coupled calcium oscillators

Horacio G. Rotstein, Rachel Kuske

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


In this paper we consider the mechanism for localized behavior in coupled calcium oscillators described by the canonical two-pool model. Localization occurs when the individual cells oscillate with amplitudes of different orders of magnitude. Our analysis and computations show that a combination of diffusive coupling, heterogeneity, and the underlying canard structure of the oscillators all contribute to the localized behavior. Two key quantities characterize the different states of the system by representing the effects of both the autonomous and the non-autonomous terms which are due to the coupling. By highlighting the influence of the canard phenomenon, these quantities identify stabilizing and destabilizing effects of the coupling on the localized behavior. We compare our analysis with computations, describing multi-mode states and asynchronized large oscillations in addition to the localized states.

Original languageEnglish (US)
Pages (from-to)46-61
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Issue number1
StatePublished - Mar 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Calcium oscillators
  • Canard phenomenon
  • Coupled oscillators
  • Localized oscillations
  • Mixed-mode oscillations


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