Hybrid Models and Biological Model Reduction with PyDSTool
Figure 4
Schematic of the temporal aspects of model reduction with hybrid systems.
This example assumes a model with hub-like connectivity, exhibiting multiple scale dynamics, and a periodic behavior (period ), but a similar process can be described for non-periodic dynamics. State variables are shown by boxes and their inter-coupling by lines. A) Dominant scale analysis identifies Regime I over some time window
(indicated on the blue time axis) within which a subset of the variables (yellow oval) are the most influential on the system's output; the other connections are effectively weak (dashed lines). B) The internal dynamics of the resulting sub-model for the regime (yellow puzzle piece) is analyzed in the context of known input and output conditions alongside the full model under equivalent conditions, and the parameters and contextual conditions for the reduction are tuned to maximize the accuracy of this representation over
. C) The consistency of the sub-model with the full dynamics beyond
is tested for the generation of accurate cyclic behavior over a period
for
, allowing for further refinement. D) The process in A–C is repeated for other regimes, creating four consecutive sub-models in this example. These should form a self-consistent cycle of entry and exit conditions (indicated by matching puzzle pieces) such that from the composition emerges a periodic behavior closely matching that of the full model.