On the authors' and employers' webpages: There are no format restrictions; files prepared and/or formatted by AIP or its vendors (e.g., the PDF, PostScript, or HTML article files published in the online journals and proceedings) may be used for this purpose. If a fee is charged for any use, AIP permission must be obtained. An appropriate copyright notice must be included along with the full citation for the published paper and a Web link to AIP's official online version of the abstract. A dedicated nonlinear oscillator model able to reproduce the pulse shape, refractory time, and phase sensitivity of the action potential of a natural pacemaker of the heart is developed. The phase space of the oscillator contains a stable node, a hyperbolic saddle, and an unstable focus. The model reproduces several phenomena well known in cardiology, such as certain properties of the sinus rhythm and heart block. In particular, the model reproduces the decrease of heart rate variability with an increase in sympathetic activity. A sinus pause occurs in the model due to a single, well-timed, external pulse just as it occurs in the heart, for example due to a single supraventricular ectopy. Several ways by which the oscillations cease in the system are obtained ͑models of the asystole͒. The model simulates properly the way vagal activity modulates the heart rate and reproduces the vagal paradox. Two such oscillators, coupled unidirectionally and asymmetrically, allow us to reproduce the properties of heart rate variability obtained from patients with different kinds of heart block including sino-atrial blocks of different degree and a complete AV block ͑third degree͒. Human heart rate is not constant. In fact, heart rate variability is a major factor in the effective functioning of the cardiovascular system and an important factor in medical diagnosis. A large effort has gone into defining complexity measures using both chaos theory and statistical physics concepts in order to create tools for such diagnosis. In spite of this, the source of the variability is not completely understood and remains an open research subject. It is well known that the autonomous nervous system moderates heart rate in mammals. One way to understand how this occurs is to build models. A variety of models-including the so-called whole heart modelsexist today. However, usually such models are so complex that an investigation of the global dynamical properties of the heart is difficult. Consequently, very rarely do they address the problem of heart rate variability. In our approach, we return to the 20th Century attempts of van der Pol and van der Mark of using relaxation oscillators to study the conduction system of the heart and its interaction with the autonomous nervous system. Following the work of several groups in the field, we developed our own modified van der Pol oscillator. We show that it is able to reproduce certain phenomena that occur in clinically recorded human heart rate: irregular heart rate, asystole, sinus pause, vagal paradox, certai...