A method to synchronize and control a system of parallel single-phase inverters without communication is presented. Inspired by the phenomenon of synchronization in networks of coupled oscillators, we propose that each inverter be controlled to emulate the dynamics of a nonlinear dead-zone oscillator. As a consequence of the electrical coupling between inverters, they synchronize and share the load in proportion to their ratings. We outline a sufficient condition for global asymptotic synchronization and formulate a methodology for controller design such that the inverter terminal voltages oscillate at the desired frequency, and the load voltage is maintained within prescribed bounds. We also introduce a technique to facilitate the seamless addition of inverters controlled with the proposed approach into an energized system. Experimental results for a system of three inverters demonstrate power sharing in proportion to power ratings for both linear and nonlinear loads.