Canard phenomenon has recently been suggested in the context of three-dimensional systems of singularly perturbed ordinary differential equations. Canards first introduced in terms of the classical canard phenomenon in the two-dimensional system such as van der Pol oscillator. However, this phenomenon only indicated the transition from a state of small-amplitude oscillatory created in a Hopf bifurcation to a large-amplitude relaxation oscillatory for an extremely small range of a control parameter. Therefore, two-dimensional systems show either small-amplitude oscillations (subthreshold oscillation) or large-amplitude oscillations but no MMOs. In the three-dimensional systems, a specific type of canard called canards of folded node can be the origin of MMOs. A basic insight about MMOs in this system is that a state of the system is dynamically changed from STO to a large amplitude oscillation so that the system is return from large relaxation oscillation to the basin of attraction of STO state.
(From "The Effect of Input Current on Canard-Induced Mixed-Mode Oscillation in Layer II Stellate Cell", the 10th Asian Control Conference 2015 (ASCC 2015), Kota Kinabalu, 31st May - 3rd June 2015, IEEE. Babak V.Ghaffari, M.Kouhnavard, T. Kitajima)
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