A control scheme is proposed for an islanded lowinertia three-phase inverter-based microgrid with a high penetration of photovoltaic (PV) generation resources. The output of each inverter is programmed to emulate the dynamics of a nonlinear oscillator. The virtual oscillators within each controller are implicitly coupled through the physical electrical network. The asymptotic synchronization of the oscillators can be guaranteed by design, and as a result, a stable power system emerges innately with no communication between the inverters. Time-domain switching-level simulation results for a 45-kW microgrid with 33% PV penetration demonstrate the merits of the proposed technique; in particular they show that the load voltage can be maintained between prescribed bounds in spite of variations in incident irradiance and step changes in the load.