Oscillations:

Oscillations are a useful part of what nervous systems do. Chewing and walking are two examples of rhythmic motor patterns that are a part of many organisms.

Oscillating Networks With a Pace-Maker Cell:

One way that a collection of neurons can oscillate is to have one of the neurons oscillate on its own, and have the other cells oscillate because they are told to do so (through their synaptic interactions) by the neuron that intrinsically oscillates. In this situation, we call the intrinsically oscillating neuron the "pace-maker" since it sets the pace for the entire network. But this isn't the only way to have a network that oscillates. Just as a single oscillating neuron can contain a collection of currents that don't oscillate on their own, but when they get together they start to oscillate, a network of neurons can contain only neurons that don't oscillate on their own, but when they get together they do. This is an example of an emergent property. Sometimes emergent properties are seen as spooky, imprecise things (until you've looked at them for a long time and gotten tired of feeling spooked out), and without mathematics, they are imprecise things. With mathematics, they can be made precise, but they're still a little spooky.

How Do Neurons That Don't Oscillate Get Together To Oscillate? When is the whole greater than the sum of its parts...?

What makes the system oscillate?

It wouldn't be completely honest to say that you can't get some understanding of these questions without completely understanding the mathematics involved, but by understanding the mathematics, you can gain a deeper, more reliable understanding. After all, mathematics is just the process of making your understandings of the relationships between things more precise and self-consistent.

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References:
Kandel, E., Schwartz J., and Jessel, T., (eds.) "Principles of Neural Science. Third Edition," New York: Elsevier, 1991.