In the OP, phantom power wrote "Networked Networks Are Prone to Epic Failure"
In post #6, bemildred wrote "The general theory of these things is actually pretty old."
In post #5, bananas wrote "There's tons of research on this at all levels going back decades."
Although wikipedia describes "network science" as a new discipline, the application of graph theory etc to both electric circuits and neural circuits (and other circuits) goes back a long way. The "general theory of these things" applies to both electric and neural networks, including issues of stability.
http://en.wikipedia.org/wiki/Network_scienceNetwork science is a new and emerging scientific discipline that examines the interconnections among diverse physical or engineered networks, information networks,
biological networks, cognitive and semantic networks, and social networks. This field of science seeks to discover common principles, algorithms and tools that govern network behavior. The National Research Council defines Network Science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena."
The embedded link to "biological networks" goes directly to:
http://en.wikipedia.org/wiki/Biological_neural_networkBiological neural network
In neuroscience, a neural network describes a population of physically interconnected neurons or a group of disparate neurons whose inputs or signalling targets define a recognizable circuit. Communication between neurons often involves an electrochemical process. The interface through which they interact with surrounding neurons usually consists of several dendrites (input connections), which are connected via synapses to other neurons, and one axon (output connection). If the sum of the input signals surpasses a certain threshold, the neuron sends an action potential (AP) at the axon hillock and transmits this electrical signal along the axon.
In contrast, a neuronal circuit is a functional entity of interconnected neurons that influence each other (similar to a control loop in cybernetics).
From "Texture of the Nervous System of Man and the Vertebrates" by Santiago Ramón y Cajal. The figure illustrates the diversity of neuronal morphologies in the auditory cortex. Some more reading for you:
http://en.wikipedia.org/wiki/Network_analysishttp://en.wikipedia.org/wiki/Graph_theoryhttp://en.wikipedia.org/wiki/Neural_network_%28disambiguation%29http://en.wikipedia.org/wiki/Connectednesshttp://en.wikipedia.org/wiki/Flow_networkhttp://en.wikipedia.org/wiki/Operations_research