  Many biological systems can sense periodical variations in a stimulus input
and produce well-timed, anticipatory responses after the input is removed. Such
systems show memory effects for retaining timing information in the stimulus
and cannot be understood from traditional synchronization consideration of
passive oscillatory systems. To understand this anticipatory phenomena, we
consider oscillators built from excitable systems with the addition of an
adaptive dynamics. With such systems, well-timed post-stimulus responses
similar to those from experiments can be obtained. Furthermore, a well-known
model of working memory is shown to possess similar anticipatory dynamics when
the adaptive mechanism is identified with synaptic facilitation. The last
finding suggests that this type of oscillators can be common in neuronal
systems with plasticity.
