We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $alpha$ effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale non-axisymmetric magnetic fields on the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that bipolar regions emerge due to magnetic buoyancy in situ of the large-scale dynamo action, we show that fluctuations of the $alpha$ effect can maintain the non-axisymmetric magnetic fields through a solar-type $alpha^{2}Omega$ dynamo process. It is found that diffusive decay of bipolar active regions is likely to be the primary source of the non-axisymmetric magnetic fields observed on the Sun. Our results show that the non-axisymmetric dynamo model with stochastic perturbations of the $alpha$ effect can explain periods of extremely high activity (`super-cycle events) as well as periods of deep decline of magnetic activity. We compare the models with synoptic observations of solar magnetic fields for the last four activity cycles, and discuss implications of our results for interpretation of observations of stellar magnetic activity.
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