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For flows, the singular cycles connecting saddle periodic orbit and saddleequilibrium can poten- tially result in the so-called singular horseshoe, whichmeans the existence of a non-uniformly hyperbolic chaotic invariant set.However, it is very hard to find a specific dynamical system that exhibits suchsingular cycles in general. In this paper, the existence of the singular cyclesinvolved in saddle periodic orbits is studied by two types of piecewise affinesystems: one is the piecewise affine system having an admissible saddle pointwith only real eigenvalues and an admissible saddle periodic orbit, and theother is the piecewise affine system having an admissible saddle- focus and anadmissible saddle periodic orbit. Precisely, several kinds of sufficientconditions are obtained for the existence of only one heteroclinic cycle oronly two heteroclinic cycles in the two types of piecewise affine systems,respectively. In addition, some examples are presented to illustrate theresults.

Singular cycles connecting saddle periodic orbit and saddle equilibrium in piecewise smooth systems