  We present a mechanism for the emergence of strange attractors (observable
chaos) in a two-parameter periodically-perturbed family of differential
equations on the plane. The two parameters are independent and act on different
ways in the invariant manifolds of consecutive saddles in the cycle. When both
parameters are zero, the flow exhibits an attracting heteroclinic cycle
associated to two equilibria. The first parameter makes the two-dimensional
invariant manifolds of consecutive saddles in the cycle to pull apart; the
second forces transverse intersection. These relative positions may be
determined using the Melnikov method.
  Extending the previous theory on the field, we prove the existence of many
complicated dynamical objects in the two-parameter family, ranging from "large"
strange attractors supporting SRB (Sinai-Ruelle-Bowen) measures to superstable
sinks and H\'enon-type attractors. We draw a plausible bifurcation diagram
associated to the problem under consideration and we show that the occurrence
of heteroclinic tangles is a \emph{prevalent} phenomenon.
