A spontaneously formed vortex can occur in an incoherently pumped microcavity-polariton condensate which is a non-equilibrium system. The stability of this vortex depends on the flux quanta that the vortex owns. In this paper, we have investigated the dynamics of spontaneously formed vortices with multiple-flux quanta in incoherently pumped microcavity-polariton condensates. From the excitation spectra of a spontaneously formed vortex, we can study the stability of the vortex under different pump strength. The vortices with flux quanta less than four are dynamically stable within a wide range of pump strength. However, when the flux quanta of a vortex is greater than three and the pump power is above a critical pump strength, some imaginary parts of excitation modes of the vortex become positive. The vortex then becomes dynamically unstable and Lends to split into several vortices with smaller flux quanta. (C) 2015 Elsevier Ltd. All rights reserved.
