Canards in a slow-fast continuous piecewise linear vector field

Canards are phenomena which occur in slow-fast systems when the parameter, ε, is appropriately small. An RLC circuit with a five-segment piecewise linear resistor, namely a two-dimensional five region continuous piecewise linear (CPWL) vector field, is considered. The paper discusses rigorously the canard in the four region CPWL vector field, in the case of ε→0, and verification of the boundary canard without head and canard with head in the four region.