IMPERFECT PHASE SYNCHRONIZATION IN THE LOCOMOTOR BEHAVIOR OFHALOBACTERIUM SALINARIUM

A chaotic system can be used to transform a periodic input sequence of events, e.g. impulses, into a sequence of output events. Even after transient, the output sequence is often aperiodic. In particular, it might happen that the output events are basically synchronized with the input events, but that some of them are randomly skipped from the output time series (imperfect phase synchronization [Zacks et al., 1999, 2000]). This phenomenon has been neatly observed by Schimz and Hildebrand [1992] in a rich series of experiments on the locomotor behavior of Halobacterium salinarium, where the input event was a light impulse and the output event was the reversal in the swimming direction of the bacterium. In this paper, we show that the same phenomenon occurs when classical, low dimensional chaotic oscillators are forced by a periodic sequence of impulses. This proves, on one side, that imperfect phase synchronization is a common phenomenon in chaotic oscillators subjected to periodic sequences of impulses, and, on the other side, that there are high chances that the locomotor behavior of Halobacterium salinarium can be modeled by a low dimensional deterministic model.