We analyze the dynamical mechanisms underlying the formation of arrhythmogenic early afterdepolarizations (EADs) in two mathematical models of cardiac cellular electrophysiology: the Sato et al. biophysically detailed model of a rabbit ventricular myocyte of dimension 27 and a reduced version of the Luo-Rudy mammalian myocyte model of dimension 3. Based on a comparison of the two models, with detailed bifurcation analysis using spike-counting techniques and continuation methods in the simple model and numerical explorations in the complex model, we locate the point where the first EAD originates in an unstable branch of periodic orbits. These results serve as a basis to propose a conjectured scheme involving a hysteresis mechanism with the creation of alternans and EADs in the unstable branch. This theoretical scheme fits well with electrophysiological experimental data on EAD generation and hysteresis phenomena. Our findings open the door to the development of novel methods for pro-arrhythmia risk prediction related to EAD generation without actual induction of EADs.