I would like to get past my difficulty with inhibition causing action potentials. It appears to be due to the differences between ion channel gates in timing and it can result in waves of a particular frequency. It is the key to the thalamocortical system. Here are some sources for understanding the phenomenon.
Paul King (here) hints at the importance of inhibition:
In the cerebral cortex, it has been proposed that gamma frequency synchronization (40 80 Hz) comes about partially due to the push-pull between excitatory (E) and inhibitory (I) cells. The E cells excite the I cells, which inhibit the E cells. When inhibition wears off, the E cells that spike are more likely to do so at around the same time.
G Lindsay on the Neurdiness site (here) gives this more detailed but non-mathematical explanation:
The more complicated a system is, and the more its component parts counteract each other, the less likely it is that simply thinking through a conceptual model will provide the correct results. This is especially true in the nervous system, where all the moving parts can interact with each other in frequently nonlinear ways, providing some unintuitive results. For example, the Hodgkin-Huxley model demonstrates a peculiar ability of some neurons: the post-inhibitory rebound spike. This is when a cell fires (counterintuitively) after the application of an inhibitory input. It occurs due to the reliance of the sodium channels on two different mechanisms for opening, and the fact that these mechanisms respond to voltage changes on a different timescale. This phenomenon would not be understandable without a model that had the appropriate complexity (multiple sodium channel gates) and precision (exact timescales for each). So, building models is not a fundamentally different approach to science; we do it every time we infer some kind of functional explanation for a process. However, formalizing our models in terms of mathematics allows us to see and understand more minute and complex processes.
There is a mathematical explanation and model in the Intro to CHS part 1 (here) of Hodgkin-Huxley. It is probably somewhat simpler than the actual thalamocortical loop but is a stepwise explanation with graphs of the parameters. It builds to a finely timed train of impulses. Follow the link if you want to look at the detail.