Biological rhythms are fundamental for the understanding of the physiological functioning of organisms, being useful in disease prevention and treatments. This work deals with the analysis of cardiac rhythms evaluating the electrical activity of the heart based on ECG observations. A mathematical model composed by three nonlinear oscillators coupled by time-delayed connections is employed for heartbeat description. Numerical simulations reproduce synthetic ECGs with a broad variety of responses, including normal and pathological rhythms. Atrial flutter, atrial fibrillation, ventricular flutter and two different kinds of ventricular fibrillation are investigated showing the model capability to capture the general functioning of the heart dynamics. Nonlinear tools are employed in order to help the physiology understanding, being potential interesting to help the characterization of the different behaviors. In this regard, Poincaré maps and bifurcation analysis are of concern. Poincaré maps can highlight dynamical characteristics of each rhythm while bifurcation analysis can be useful to investigate the routes from normal functioning to pathologies, which can be useful to establish an early identification of critical situations. In general, results show that dynamical perspective can be useful for physiology comprehension that can also help to pathology characterization.