Bubbling of attractors and synchronisation of chaotic oscillators

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We present a system of two coupled identical chaotic electronic circuits that exhibit a blowout bifurcation resulting in loss of stability of the synchronised state. We introduce the concept of bubbling of an attractor, a new type of intermittency that is triggered by low levels of noise, and demonstrate numerical and experimental examples of this behaviour. In particular we observe bubbling near the synchronised state of two coupled chaotic oscillators. We give a theoretical description of the behaviour associated with locally riddled basins, emphasising the role of invariant measures. In general these are non-unique for a given chaotic attractor, which gives rise to a spectrum of Lyapunov exponents. The behaviour of the attractor depends on the whole spectrum. In particular, bubbling is associated with the loss of stability of an attractor in a dynamically invariant subspace, and is typical in such systems.