The dynamical and statistical behavior of lag synchronization in two coupled self-sustained chaotic Rössler oscillators is reexamined. The lack of uniqueness in the conventional characterization of lag synchronization based on the similarity function has caused much skepticism about the existence of lag synchronization. We provide an evidence that the emergence of lag synchronization is associated with the transition from on-off intermittency to a periodic structure in the laminar phase distribution.
The complete synchronization and generalized synchronization (GS) of one-way coupled time-delay systems are studied. We find that GS can be achieved by a single scalar signal, and its synchronization threshold for different delay times shows the parameter resonance effect, i.e., we can obtain stable synchronization at a smaller coupling if the delay time of the driven system is chosen such that it is in resonance with the driving system. Near chaos synchronization, the desynchronization dynamics displays periodic bursts with the period equal to the delay time of the driven system. These features can be easily applied to the recovery of time-delay systems.
We describe a novel experiment on Rydberg atoms in crossed electric and magnetic fields, recently performed at Imperial College. The novelty resides in a combination of a crossed-field geometry with a time-gated detection technique, by which separation of the circularly polarized components is now achieved. The importance of achieving such a separation and the new opportunities it opens up are explained. By this approach, a map of the diamagnetic Stark patterns is obtained. The data exhibit interesting behaviour in that the hydrogenic and non-hydrogenic groups within the n-shell now become distinguishable. Their evolution as a function of field strength brings out the difference between linear and quadratic effects. The levels with a quadratic dependence on electric field strength eventually invade and dominate the spectrum. We surmise that the trend from order to chaos is different in crossed fields from the trend in the diamagnetic limit. We comment on further theory required to clarify this point. Our observations extend up to and slightly above the saddle-point energy.
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