Numerous calculations in diverse biological settings associate greater regularity and decreased complexity of experimental time series with disease and pathology, often accompanied by claims that such calculations indicate chaotic behavior. While the claims of chaos are unresolved, it nonetheless seems important to determine a unifying theme suggesting greater signal regularity in myriad complicated physiologic systems. Our major hypothesis is that in many systems, greater regularity corresponds to greater component autonomy and isolation. The idea is that healthy systems have good lines of communication, whereas crucial biologic messages in diseased states are either slow to transmit and receive or unable to arrive. We employ ApEn, approximate entropy, to quantify regularity and confirm the hypothesis via analysis of several very different, representational mathematical model forms, conferring a robustness to model form of the hypothesis. This hypothesis is experimentally verifiable in settings where some of the crucial network nodes and connections are known.