Effect of attractor on the desynchronization events in coupled chaotic circuits

Resumo

The phenomenon of attractor bubbling consists in incomplete or imperfect synchronization between two coupled chaotic oscillators, which synchronization regime is broken for brief escapes of different sizes.Here, we use as oscillators two chaotic electronic circuits coupled through unidirectional linear feedback in the regime of moderate coupling to study the occurrence of attractor bubbling in this system. For two different dynamical states, the system exhibits different chaotic attractors. Analysing temporal series, we build empirical distributions of the amplitudes of desynchronization events for different values of the coupling parameter. We observe that in the regime of attractor bubbling the distributions are characterized by a heavy tail, bearing similarity to the ones observed in complex systems with self-organized criticality. A given heavy-tailed distribution is exhibited by the two chaotic states for different coupling strengths. We explain this effect of the attractor shape on the statistics of the desynchronization as caused by a region of instability, which is more often visited for one of the attractors than it is by the other.