Experimental evidence of locally intermingled basins of attraction in coupled Chuaʹs circuits

We show experimentally that two coupled chaotic systems initially operating on two different simultaneously co-existing attractors can be synchronized. Synchronization is achieved as one of the systems switches its evolution to the attractor of the other one. The final attractor of the synchronized state strongly depends on the actual position of trajectories on their attractors at the moment when coupling is introduced. Coupling introduced in such systems can lead to the locally intermingled basins of attraction of coexisting attractors. Even if the initial location of trajectories on attractors A1 and A2 is known with infinite precision, we are unable to determine, on the basis of any finite calculation, in which basin this location lies and finally we cannot be sure on which attractor the evolution will synchronize. We investigate this uncertainty in chaos synchronization in numerical and experimental studies of two coupled Chuaʹs circuits.