Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators

Many natural and human-made nonlinear oscillators exhibit the ability to adjust their rhythms due to weak interaction: two lasers, being coupled, start to generate with a common frequency; cardiac pacemaker cells fire simultaneously; violinists in an orchestra play in unison. Such coordination of rhythms is a manifestation of a fundamental nonlinear phenomenon--synchronization. Discovered in the 17th century by Christiaan Huygens, it was observed in physics, chemistry, biology and even social behaviour, and found practical applications in engineering and medicine. The notion of synchronization has been recently extended to cover the adjustment of rhythms in chaotic systems, large ensembles of oscillating units, rotating objects, continuous media, etc. In spite of essential progress in theoretical and experimental studies, synchronization remains a challenging problem of nonlinear sciences.