  For flows, the singular cycles connecting saddle periodic orbit and saddle
equilibrium can poten- tially result in the so-called singular horseshoe, which
means the existence of a non-uniformly hyperbolic chaotic invariant set.
However, it is very hard to find a specific dynamical system that exhibits such
singular cycles in general. In this paper, the existence of the singular cycles
involved in saddle periodic orbits is studied by two types of piecewise affine
systems: one is the piecewise affine system having an admissible saddle point
with only real eigenvalues and an admissible saddle periodic orbit, and the
other is the piecewise affine system having an admissible saddle- focus and an
admissible saddle periodic orbit. Precisely, several kinds of sufficient
conditions are obtained for the existence of only one heteroclinic cycle or
only two heteroclinic cycles in the two types of piecewise affine systems,
respectively. In addition, some examples are presented to illustrate the
results.
