One‐parametric families of canard cycles: two explicitly solvable examples

Systems of singularly perturbed autonomous ordinary differential equations possessing in a parameter plane two intersecting bifurcation curves connected with the generation of limit cycles with large and small amplitude respectively, have a special class of limit cycles called canards or french ducks describing an exponentially fast transition from a small amplitude limit cycle to limit cycle with a large amplitude. We present two explicitly integrable examples of non‐autonomous singularly perturbed di.erential equations with canard cycles without a second parameter.