Phase-locking behavior and irregular dynamics were studied in a mathematical model of the sinus node driven with repetitive vagal input. The central region of the sinus node was simulated as a 15 x 15 array of resistively coupled pacemakers with each cell randomly assigned one of 10 intrinsic cycle lengths (range 290-390 msec). Coupling of the pacemakers resulted in their mutual entrainment to a common frequency and the emergence of a dominant pacemaker region. Repetitive acetylcholine (ACh; vagal) pulses were applied to a randomly selected 60% of the cells. Over a wide range of stimulus intensities and basic cycle lengths, such perturbations resulted in a large variety of stimulus/response patterns, including phase locking (1 ; 1,3 : 2, 2 : 1 , etc.) and irregular (i.e., chaotic) dynamics. At a low ACh concentration (1 fiM), the patterns followed the typical Farey sequence of phase-locked behavior. At a higher concentration (5 ftM), period doubling and aperiodic patterns were found. When a single pacemaker cell was perturbed with repetitive ACh pulses, qualitatively similar results were obtained. In both types of simulation, chaotic behavior was investigated using phase-plane ( Received December 7, 1988; accepted June 2,1989. randomly selected 20% of the cells. Such external perturbation resulted in a shift of the dominant pacemaker site and a decrease in apparent conduction velocity within the pacemaker array, which mimicked very accurately the response patterns of the mammalian heart rate to vagus nerve stimulation. 6 -7 Repetitive vagal input is capable of entraining the already mutually entrained pacemaker array in a harmonic fashion similar to that seen previously 4 for single cells. In fact, depending on the frequency of the ACh input, zones of stable phase-locking rhythms (1 : 1,2:1, etc.) may be separated by regions in which extremely irregular behavior can predominate. Several questions arise from the study of these phenomena that may have importance in the quantitative description of the heart rhythm and its alterations. First, is it possible to analyze and describe this very complex aperiodic behavior in a quantitative but nonstatistical form? Second, can the transition ("road") between ordered (i.e., 1 : 1,