  The canard explosion is the change of amplitude and period of a limit cycle
born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon
is well understood in singular perturbation problems where a small parameter
controls the slow/fast dynamics. However, canard explosions are also observed
in systems where no such parameter is present. Here we show how the iterative
method of Roussel and Fraser, devised to construct regular slow manifolds, can
be used to determine a canard point in a general planar system of nonlinear
ODEs. We demonstrate the method on the van der Pol equation, showing that the
asymptotics of the method is correct, and on a templator model for a
self-replicating system.

Dynamical Systems