202207271958 Stability or instability dominates a system

When undertaking a simulation or evaluating a system for its effectiveness or accuracy, it’s important to look closely at whether stability or instability (do small changes result in large differences in outcomes) dominate the problem. It will determine if the results are valuable or even impossible to find.¹

Related to this is whether the 202207272000 Garbage in, garbage out rule of thumb is applicable to the system in question. If a system has strong stabilizing or converging forces it can accept "garbage" as input and give great results. Conversely a system with strong diverging, destabilizing forces can accept extremely precise inputs and still produce nonsense.

Note: we can actually use the instability of such systems as a guide for a numeric/iterative approach to getting good results. If we see a large jump in results after a few iterations or steps, we might be able to conclude that we've "strayed too far" and are under the influence of the strong divergence, which in turn tells us to "re-evaluate" some of the most recent steps more carefully. This is known as a predictor-corrector.