Assume a nonlinear dynamical system depending on some control parameters.
Assume you want to study if the system is critically slowing down or undergoing some critical transition in general.
Besides studying how autocorrelation at lag 1 and first (two) moments change over time, what would you study? Can you point to papers related to early warning signals?
Cc: @johncarlosbaez @j_bertolotti @lmrocha @lamaral @thilo @c4computation @tchambers
An off-center, conceptual treatment of biological senescence (as a system-level transition) by Rosen Congress to mind:
https://www.sciencedirect.com/science/article/abs/pii/S0304020808712258
https://link.springer.com/article/10.1007/BF02461066
More generally, the Rosen view is that in complex systems, model failure is a signal that the system is undergoing a transition---i.e. when past data suddenly does not work well to predict the present (think the failure of Google flu). But precise measures of model failure before it happens are not around, besides what you mention (e.g. à la Marten Scheffer).
@johncarlosbaez @j_bertolotti @lamaral @thilo @c4computation @tchambers
@lmrocha @johncarlosbaez @j_bertolotti @lamaral @thilo @c4computation @tchambers i will read them. The abstracts sound so cryptic.. But that's Rosen style, I guess.