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A novel possibility of self-organized behaviour of stochastically drivenoscillators is presented. It is shown that synchronization by L\'evy stableprocesses is significantly more efficient than that by oscillators withGaussian statistics. The impact of outlier events from the tail of thedistribution function was examined by artificially introducing a few additionaloscillators with very strong coupling strengths and it is found that remarkablyeven one such rare and extreme event may govern the long term behaviour of thecoupled system. In addition to the multiplicative noise component, we haveinvestigated the impact of an external additive L\'evy distributed noisecomponent on the synchronisation properties of the oscillators.

Self-organisation of random oscillators with L\'evy stable distributions