Can-annular combustors consist of N distinct cans setup symmetrically around the axis of the gas turbine. Each can is connected to the turbine inlet by means of a transition duct. At the turbine inlet, a small gap between the neighboring transition ducts allows acoustic communication between the cans. Thermoacoustic pulsations in the cans are driven by the respective flames, but also the communication between neighboring cans through the gap plays a significant role. In this study, we focus 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, 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 nonlinear solution in a probabilistic sense. One outcome of these simulations is the various pulsation patterns, which are in principle different from one can to the next. We recover how not only a stronger flame response in one can gives 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 mode shape. We finally predict the coherence and phase between cans on the linearized system subject to noise, and compare the predictions with engine measurements, in terms of spectra of amplitude in each can and coherence and phase, observing a good match.