We extend a model of the evanescent field-coupled multi-core Yb-doped fiber laser to include fluctuations of the level populations with the goa lof determining the stability properties of collective modes. The nonlinear differential equations for light intensity, the phases of the electric fields, and the occupation number of the upper laser level of each core are integrated numerically, while, for two cores the relaxation rates, oscillation frequencies, and stability criteria are determined analytically from the set of linearized equations. For example, for two identical lasers we find the in-phase super mode to be unstable in the range 0<κ/Δβnl<1, where κ is the inter-guide coupling constant and Δβnl the non-linear change in the mode propagation constant. The system is bi-stable for |κ/Δβnl|>1, and we describe how switching can be performed. Besides evanescent-field coupled lasers the analysis may be applicable to other coupling mechanisms, such as external cavities, although with some caution.