In this paper, we develop a physiological oscillator model of which the output mimics the shape of the R-R interval Poincare plot. To validate the model, simulations of various nervous conditions are compared with heart rate variability (HRV) data obtained from subjects under each prescribed condition. For a variety of sympathovagal balances, our model generates Poincare plots that undergo alterations strongly resembling those of actual R-R intervals. By exploiting the oscillator basis of our model, we detail the way that low- and high-frequency modulation of the sinus node translates into R-R interval Poincare plot shape by way of simulations and analytic results. With the use of our model, we establish that the length and width of a Poincare plot are a weighted combination of low- and high-frequency power. This provides a theoretical link between frequency-domain spectral analysis techniques and time-domain Poincare plot analysis. We ascertain the degree to which these principles apply to real R-R intervals by testing the mathematical relationships on a set of data and establish that the principles are clearly evident in actual HRV records.