  The stability of heteroclinic cycles may be obtained from the value of the
local stability index along each connection of the cycle. We establish a way of
calculating the local stability index for quasi-simple cycles: cycles whose
connections are 1-dimensional and contained in flow-invariant spaces of equal
dimension. These heteroclinic cycles exist both in symmetric and non-symmetric
contexts. We make one assumption on the dynamics along the connections to
ensure that the transition matrices have a convenient form. Our method applies
to all simple heteroclinic cycles of type Z and to various heteroclinic cycles
arising in population dynamics, namely non-simple heteroclinic cycles, as well
as to cycles that are part of a heteroclinic network. We illustrate our results
with a non-simple cycle present in a heteroclinic network of the
Rock-Scissors-Paper game.
