It has recently been shown that the PEC (partially extending strand convection) model of Larson is able to describe thixotropic yield stress behavior in the limit where the relaxation time is large. In this paper, we discuss the behavior of the model under an imposed periodic shear force tau(t) =A + B sin(omega t - Phi). We identify regimes of fast, slow and yielded dynamics and discuss the overall behavior of the system in dependence of the parameters A, B, omega and Phi. The method of averaging turns out to be a crucial mathematical tool for the analysis. The scale of the period of the oscillation relative to the times over which yielding and unyielding occur has a crucial influence on the qualitative dynamics. (C) 2014 Elsevier B.V. All rights reserved.