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We study the statistics of the amplitude of the synchronization error inchaotic electronic circuits coupled through linear feedback. Depending on thecoupling strength, our system exhibits three qualitatively different regimes ofsynchronization: weak coupling yields independent oscillations; moderate tostrong coupling produces a regime of intermittent synchronization known asattractor bubbling; and stronger coupling produces complete synchronization. Inthe regime of moderate coupling, the probability distribution for the sizes ofdesynchronization events follows a power law, with an exponent that can beadjusted by changing the coupling strength. Such power-law distributions areinteresting, as they appear in many complex systems. However, most of thesystems with such a behavior have a fixed value for the exponent of the powerlaw, while here we present an example of a system where the exponent of thepower law is easily tuned in real time.

Tunable power law in the desynchronization events of coupled chaotic electronic circuits