This study analyzes parallel inverter control methods derived from two distinct second-order nonlinear differential models: the Van der Pol and Andronov-Hopf oscillators. These mathematical formulations establish voltage magnitude and frequency references, forming a resilient nonlinear droop mechanism that facilitates inverter coordination in the absence of communication links. The control algorithm is designed to achieve power sharing and synchronization of voltage and frequency among inverters. Compared to the Van der Pol oscillator, the Andronov-Hopf model delivers enhanced overall performance, characterized by more effective power sharing, reduced harmonic content, and quicker dynamic response. The calculation results are obtained using the period - averaging method, with simulation scenarios conducted in MATLAB Simulink.