Journal article
Amplitude-modulated spiking as a novel route to bursting: Coupling-induced mixed-mode oscillations by symmetry breaking
Department of Applied Mathematics and Computer Science, Technical University of Denmark1
Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark2
Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3
Mixed-mode oscillations consisting of alternating small- and large-amplitude oscillations are increasingly well understood and are often caused by folded singularities, canard orbits, or singular Hopf bifurcations. We show that coupling between identical nonlinear oscillators can cause mixed-mode oscillations because of symmetry breaking.
This behavior is illustrated for diffusively coupled FitzHugh-Nagumo oscillators with negative coupling constant, and we show that it is caused by a singular Hopf bifurcation related to a folded saddle-node (FSN) singularity. Inspired by earlier work on models of pancreatic beta-cells [Sherman, Bull.
Math. Biol. 56, 811 (1994)], we then identify a new type of bursting dynamics due to diffusive coupling of cells firing action potentials when isolated. In the presence of coupling, small-amplitude oscillations in the action potential height precede transitions to square-wave bursting. Confirming the hypothesis from the earlier work that this behavior is related to a pitchfork-of-limit-cycles bifurcation in the fast subsystem, we find that it is caused by symmetry breaking.
Moreover, we show that it is organized by a FSN in the averaged system, which causes a singular Hopf bifurcation. Such behavior is related to the recently studied dynamics caused by the so-called torus canards.
Language: | English |
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Publisher: | AIP Publishing LLC |
Year: | 2022 |
Pages: | 013121 |
ISSN: | 10897682 and 10541500 |
Types: | Journal article |
DOI: | 10.1063/5.0072497 |
ORCIDs: | 0000-0002-2639-2394 , Brøns, Morten and Sørensen, Mads Peter |