We construct a model of cell reprogramming (the conversion of fully differentiated cells to a state of pluripotency, known as induced pluripotent stem cells, or iPSCs) which builds on key elements of cell biology viz. cell cycles and cell lineages. Although reprogramming has been demonstrated experimentally, much of the underlying processes governing cell fate decisions remain unknown. This work aims to bridge this gap by modelling cell types as a set of hierarchically related dynamical attractors representing cell cycles. Stages of the cell cycle are characterised by the configuration of gene expression levels, and reprogramming corresponds to triggering transitions between such configurations. Two mechanisms were found for reprogramming in a two level hierarchy: cycle specific perturbations and a noise induced switching. The former corresponds to a directed perturbation that induces a transition into a cycle-state of a different cell type in the potency hierarchy (mainly a stem cell) whilst the latter is a priori undirected and could be induced, e.g. by a (stochastic) change in the cellular environment. These reprogramming protocols were found to be effective in large regimes of the parameter space and make specific predictions concerning reprogramming dynamics which are broadly in line with experimental findings.