The blade vibration level of an aerodynamically unstable rotor is a quantity of crucial importance to correctly estimate the blade fatigue life. This amplitude is the result of the balance between the energy pumped into the blades by the gas flow, and the nonlinear dissipation at the blade-disk contact interfaces. In a tuned configuration, the blade displacements can be described as a travelling wave consisting of one fundamental nodal diameter and frequency and its higher harmonics, and the problem can be reduced to the computation of a time periodic solution in just one sector. This simplification is no longer valid for a mistuned bladed disk. The resulting nonlinear vibration of the mistuned system is a combination of several travelling waves with different number of nodal diameters, coupled through mistuning. In this case, the complete bladed disk has to be considered, which requires an extremely high computational cost, and, for this reason, reduced order models (ROM) are required to analyze this situation. In this work, we use a 3 DOF/sector mass-spring system to describe the nonlinear friction saturation of the flutter vibration amplitude of a realistic mistuned bladed disk. The convergence of the solution of the mass-spring system is still quite slow because of the presence of many unstable modes with very similar growth rates. In order to speed-up the simulations a simpler asymptotic ROM is derived from the mass-spring model, which allows for much faster integration times. The simulations of the asymptotic ROM are compared with the measurements obtained in the European project FUTURE, where an aerodynamically unstable LPT rotor was tested with different intentional mistuning patterns.