Can-annular combustors consist of N distinct cans set up symmetrically around the axis of the gas turbine rotor. Each can is connected to the turbine inlet by means of a transition duct. At the turbine inlet a small gap between the neighbouring transition ducts allows acoustic communication between the individual cans. Thermoacoustic pulsations in the cans are driven by the respective flames, but also the communication between neighbouring cans through the gap plays a significant role. In this study we focus in particular on the effect of the background noise intensity and of the nonlinear flame saturation. We predict how usually clusters of thermoacoustic modes are unstable in the linear regime and compete with each other in the nonlinear regime, with each cluster consisting of axial, azimuthal and push-pull modes. Since linear theory cannot predict the nonlinear solution, stochastic simulations are run to study the non-linear solution in a probabilistic sense. One outcome of these simulations are the various pulsation patterns, which are in principle different from one can to the next. This is done for several configurations, with a focus on the effect of a loss of rotational symmetry of the system. We recover how a stronger flame response in one can give rise to the phenomenon of mode localization, but also how the nonlinearity of the flame saturation and the competition between modes have an effect on the nonlinear average mode shape. We finally predict the coherence and phase pattern between cans on the linearized system subject to stochastic noise, and compare the predictions with direct engine measurements, both in terms of spectra of pulsation amplitude in each can and coherence and phase between different cans, observing a good match.