Wiggly canards: Growth of traveling wave trains through a family of fast-subsystem foci

<p style='text-indent:20px;'>A class of two-fast, one-slow multiple timescale dynamical systems is considered that contains the system ordinary differential equations obtained from seeking travelling-wave solutions to FitzHugh-Nagumo in one space dimension. The question addressed mechanism by which a small-amplitude periodic orbit, created Hopf bifurcation, undergoes rapid amplitude growth small parameter interval, akin <i>canard explosion</i>. presence saddle-focus structure around slow manifold implies single orbit sequence folds as grows. An analysis performed under some general hypotheses using combination ideas theory canard explosion and Shilnikov analysis. asymptotic formula for dependence location on singular parameters control saddle focus eigenvalues. shown agree with numerical results both synthetic normal-form example system.</p>