Replicated by Mohammad Mojtahedzadeh from Alan Graham’s thesis, or created anew with the same inspiration. He created these models in the course of his thesis work on structural analysis through pathway participation matrices.
These models are pure positive feedback loops that don’t exhibit exponential growth (under the right initial conditions). See my blog post for a discussion of the details.
These are generic models, and therefore don’t have units. All should run with Vensim PLE, except the generic gain matrix version which uses arrays and therefore requires an advanced version or the Model Reader.
The original 4th order model, replicated from Alan’s thesis: PurePosOscill4.vpm – note that this includes a .cin file with an alternate stable initialization.
My slightly modified version, permitting initialization with different gains at each level: PurePosOscill4alt.vpm
Loops of different orders: 3.vpm 6.vpm 8.vpm 12.vpm (I haven’t spent much time with these. It appears that the high-order versions transition to growth rather quickly – my guess is that this is an artifact of numerical precision, i.e. any tiny imprecision in the initialization introduces a bit of the growth eigenvector, which quickly swamps the oscillatory signal. It would be interesting to try these in double precision Vensim to see if I’m right.)
A generic version, representing a system as a generic gain matrix, so you can use it to explore any linear unforced variant: Generic.vpm