Self-organisation of random oscillators with Lévy stable distributions

A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by L\'{e}vy stable processes is significantly more efficient than that by oscillators with Gaussian statistics. The impact of outlier events from the tail of the distribution function was examined by artificially introducing a few additional oscillators with very strong coupling strengths and it is found that remarkably even one such rare and extreme event may govern the long term behaviour of the coupled system. In addition to the multiplicative noise component, we have investigated the impact of an external additive L\'{e}vy distributed noise component on the synchronisation properties of the oscillators