Brain rhythms provide a wonderful playground for those interested in
applying nonlinear dynamics to systems and cognitive neuroscience. Their
importance has been highlighted in a range of functions including
working memory, attention and navigation. But the origin of these
rhythms and how they respond to stimuli are still open questions in many
systems, as is their role in inter-areal communication strategies: what
information are they conveying? I will review various nonlinear
mechanisms for oscillation, paying special attention to distinguishing
endogeneous rhythms from forced ones, and to stochastic effects. I will
present a recent theory on the burstiness of rhythms: how they often
present in brief epochs. Finally I will discuss inference techniques to
decipher the circuitry behind rhythms from data, an effort that could
eventually lead to a personalized medicine approach to correcting faulty
rhythms.