The bifurcation analysis of heteroclinic chains is important for many
applications; such chains arise for example in biological or physical
models, and their existence is often connected with a rich variety of nearby
dynamics. Recently, some of the theoretical and computational tools for the
analysis of heteroclinic chains connecting hyperbolic equilibria have been
extended to chains connecting hyperbolic equilibria and hyperbolic periodic
orbits. The analytical results obtained via an extension of Lin's method can
readily be applied to an equilibrium-to-periodic-orbit cycle (EtoP cycle),
giving rise to bifurcation equations for homoclinic orbits near the EtoP
cycle. These homoclinic bifurcations and their relation to the EtoP cycle
are confirmed by numerical evidence, which is obtained by a computational
method to find and continue EtoP connections in parameters. This numerical
method is based on the theoretical framework of Lin's method and is also
discussed in this talk.