Interestingly, in the same context of multiple time scale problems, the approach can be slightly modified to provide initial conditions on the slow manifold with prescribed coarse-scale observables.
The new transformation of jointly varying endpoints into separated endpoints will also find applications in the continuous time problems or time scales problems (see, e.g., [15]).
Geometric singular perturbation theory (GSPT) [2 9] forms the mathematical foundation behind this approach and it is a well-established tool in the analysis of many multiple time scales problems in the biosciences (see, e.g., [1, 10 12]).
Maudlin considers the time-scale problem pointed to by other writers, and concludes, contra Dennett, that the extreme slowness of a computational system does not violate any necessary conditions on thinking or consciousness.
Interestingly, this results in the same resting state ( I syn = 0 ) singular limit geometry as the 4-fast/1-slow time-scale problem used here to analyze the current step protocol (Fig. 12).
This makes sense because considering s fast allows the manifold { s = 0 } to be reached on a fast time-scale, and thus the system reduces to the same 4-fast/1-slow time-scale problem used here.
For this extended time-scale problem, uncertainty of renewable generation and load forecast is quantified with probability distribution and confidence levels are used to establish likelihood of forecast error.
This suggests an inherent three time-scales problem.
"These are such long time-scale problems that we're grappling with.
For example averaging techniques are particularly useful for long time-scale problems, such as low thrust transfers or space debris evolution, in order to provide high speed simulations with good differentiability features.
Multiple (or slow fast) time-scale problems are usually modelled by singularly perturbed systems such as (1) where the time-scale separation of the 'fast' variable v (voltage) and the 'slow' variable w (recovery variable) is explicitly identified through the singular perturbation parameter (varepsilon ll1).
