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| As it is well-known, the basis of most neuron models is to assume that a neuron behaves in first approximation as an electrical circuit.
Moreover, electrical circuits have been shown to be faithfully modeled by piecewise linear systems. On the other hand, neuron models are characterized by different time scales, and canard phenomena (explosions, complex oscillations,...), have been extensively investigated in the context of smooth mathematical models of neuron.
For that reason, we consider an interesting task the study of the existence of canards in piecewise linear slow-fast systems.
In this work, we take a first step in this direction, by analyzing the existence of canard orbits in a family of planar slow-fast piecewise linear systems with three zones of linearity. In the near future, the purpose is trying to use the results obtained to provide models of neurons equally efficient to the smooth models, offering better mathematical tractability. |
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