We investigate the dynamics near a heteroclinic cycle between a hyperbolic equilibrium E and a hyperbolic periodic solution P such that both connections are of codimension one. Such a cycle can be seen as the center of a two-parameter bifurcation scenario and, depending on properties of the transition maps, we find different types of (chaotic) shift dynamics near the cycle. Through our study we further explore the bifurcation diagrams previously outlined by others. In particular, we identify multipulse-homoclinic solutions to E and P that take more than one turn around the cycle before converging to E or P.

These results are joint work with Alexandre Rodrigues (Porto) and appear in Nonlinearity 30 (6).