In this study, a second-order model to approximate the behavior of a DC microgrid operating in the island mode is described. The main objective of this research is to analyze the system stability and demonstrate the presence of Hopf bifurcations under certain operating conditions that lead to periodic orbits. This feature arises from the interaction among the nonlinear elements of the system, such as nonlinear and active loads, and the network topology. The stability analysis results show that the system stability depends on the operating conditions and can become unstable in certain situations, exhibiting periodic orbits. The findings of this study can assist in designing more effective control strategies to enhance the stability of isolated DC microgrids under various operating conditions, which is important for the development of sustainable and reliable renewable energy systems. Keywords: Bifurcation, Droop Control, Flow, Microgrid, Periodic Orbits, Equilibrium Point DOI： https://doi.org/10.35741/issn.0258-2724.58.5.19