Canards and irregular oscillations in a nonlinear circuit

Slow-fast systems appear when some parameter takes relatively small values compared to the other parameters of the system. Canard is the name of certain singular solutions of slow-fast systems. Some interesting properties and the existence of canards are shown by using nonstandard analysis. One feature of canards is that the range of the parameters corresponding to them is very narrow. This sometimes causes discontinuous and rough behavior changes in numerical solutions. Another feature is that canards have structural instability, that is, they are easily destroyed by a perturbation. The authors explain the strange behavior of a nonlinear circuit with a small parameter