oscillators - Is there a relation between large-scale oscillations and small-scale oscillations?

From Neural oscillation - Wikipedia:

Oscillatory activity in the brain is widely observed at different levels of organization and is thought to play a key role in processing neural information.

In general, is there a relation between large-scale oscillations and small-scale oscillations? How are the "larger" ones created from "smaller" ones? I think it must relate to coupled oscillations in small-scale, is that correct? Does it behave like the creation - annihilation in quantum mechanics? How would one describe all the large and small ones in one framework?

^{Related: Is there a difference between physiological stimulations and psychological stimulations?}

Answer

Yes, there is. The keywords you're looking for are collective behavior and, in particular, synchronization in dynamical systems. And yes again: there must be some sort of coupling and, in a discrete model, the coupling between the individual oscillators will typically take the form of a synchronization network.

A recent (2015) review is Synchronization of chaotic systems, by Pecora and Carroll, and probably also worth mentioning are the book Dynamical System Synchronization by Luo and the highly-cited 2002 review The synchronization of chaotic systems by Boccaletti et al., but there's plenty of material on-line.

The last two questions are most interesting and unfortunately I can answer little more than to say that, yes, I think there might be a field theoretical approach to the problem, but all I could find in a quick search is the work of Ovchinnikov on Topological field theory of dynamical systems (paper II) (arxiv I, arxiv II).