Nonlinear dynamical systems such as weakly coupled oscillators are an interesting approach to be adopted for the regulation of power inverters inside microgrids. Aiming at the synchronization and load sharing in islanded mirogrid, this paper is inspired by oscillator synchronization property to propose a Hopf oscillator controller for the single-phase inverters. The Hopf oscillator dynamic equations are used for providing the inverter's frequency and amplitude voltage references which lead to a robust nonlinear droop behavior for driving the system without using communications. The Hopf oscillator provides better sharing of the load between inverters with higher robustness, less harmonic distortion, and faster time response of the associated limit cycle than the achieved by the other approach made with a Van der Pol oscillator. In addition, global asymptotic synchronization of system is proven by Lyapunov approach. Simulation results of a system composed by paralleled inverters are provided and compared with a Van der Pol oscillator approach reported in literature. Experimental results are also provided to prove the Hopf oscillator based controller under different circumstances.