Artificial biological pacemakers were developed and tested in canine ventricles. Next steps will require obtaining oscillations sensitive to external regulations, and robust with respect to long term drifts of expression levels of pacemaker currents and gap junctions. We introduce mathematical models intended to be used in parallel with the experiments.The models describe human mesenchymal stem cells (hMSC ) transfected with HCN2 genes and connected to myocytes. They are intended to mimic experiments with oscillation induction in a cell pair, in cell culture and in the cardiac tissue. We give examples of oscillations in a cell pair, in a one dimensional cell culture and dependence of oscillation on number of pacemaker channels per cell and number of gap junctions. The models permit to mimic experiments with levels of gene expressions that are not achieved yet and to predict if the work to achieve this levels will significantly increase the quality of oscillations. This give arguments for selecting the directions of the experimental work. Impressive results were obtained with stem cells to create an artificial biological pacemaker [4]: human mesenchymal stem cells (hMSC) transfected with HCN2 genes injected in canine left bundle branch provide ventricular escape rhythms that were mapped to the site of the injection. This experimental success shows great promises for future therapy.In a recent review article [5], the question : "What characteristics should be embodied in a biological pacemaker?" was put forward. The creation of a stable physiological rhythm was listed as one of the most important properties for future biopacemakers. The present article describes the mathematical models intended to be runned in parallel with the experiments to achieve this goal.The oscillations should be reasonably stable with respect to inevitable variations of the parameters affecting the biological pacemaker. Indeed, many factors can affect the period of the pacemaker namely: decreasing the expression levels of pacemaker channels or gap junctions, modification of the peptides regulating gene expressions, loss of genes, migration of small percentage of stem cells to other sites or differentiation into other cell types; loss of pacemaker function by some cells.In order to obtain a stable pacemaker, many time consuming experiments should be performed. In exploring such systems, we believe that an adequate combination of experiments with theoretical predictions can lead to a much faster results, by reaching a better quantitative understanding and in so doing, in reducing the number of