TY - JOUR
T1 - Localized and asynchronous patterns via canards in coupled calcium oscillators
AU - Rotstein, Horacio G.
AU - Kuske, Rachel
N1 - Funding Information:
The authors want to thank Nancy Kopell, Martin Wechselberger and Martin Krupa for reading earlier versions of this manuscript. This work was partially supported by the Burroughs Wellcome Fund (HGR), NSF-DMS 021505 (HGR), NSF-DMS 0072311 (RK) and a NSERC discovery grant (RK). Appendix A
PY - 2006/3/1
Y1 - 2006/3/1
N2 - 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.
AB - 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.
KW - Calcium oscillators
KW - Canard phenomenon
KW - Coupled oscillators
KW - Localized oscillations
KW - Mixed-mode oscillations
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U2 - 10.1016/j.physd.2006.01.007
DO - 10.1016/j.physd.2006.01.007
M3 - Article
AN - SCOPUS:33644925550
SN - 0167-2789
VL - 215
SP - 46
EP - 61
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1
ER -