Spatiotemporal patterns in neural networks
Unfortunately, I haven't looked at this sort of literature for a long time, but here are some thoughts with which to start.

Your question is about "spatiotemporal patterns" of neural systems. One of the first things that comes to mind is neural oscillations (e.g. alpha waves). This is essentially looking for the presence of "frequency patterns" in the neural system. This has a huge amount of literature.

Another methodology that comes to mind is the graph-theoretic approach. In essence, functional or anatomical activity is used to build a graph, which can be analyzed for patterns (i.e. special properties of the graphs of neural systems that are, say, shared across species). One paper: Complex brain networks: graph theoretical analysis of structural and functional systems by
Bullmore and Sporns.

Separately, I might think about the neural correlations literature. Essentially, this is analyzing a neural population by examining the correlation structure of its members, and looking for patterns within it (i.e. that characterize the population code of the system). Two review papers: Neural correlations, population coding, and computation by Averbeck et al
and Measuring and interpreting neural correlations by Cohen and Kohn.
For a review on population codes, see Information processing with population codes by Pouget et al.
This notion is sort of orthogonal to the notion of sparse coding in neural networks, more prevalent in sensory perception.

Sorry if this is broad, but then again I feel the question is quite broad as well. If you have more specific questions, let me know.