A system dynamics model archive
I became aware of this neat model via the Vensim forum. I have no idea what the physical basis is, but the diverse and beautiful output it generates is quite amazing.
Interestingly, if you only looked at time series of this sequence, you’d probably never notice it.
This runs in any version of Vensim. gumowski mira.mdl
I just picked up a copy of Hartmut Bossel’s excellent System Zoo 1, which I’d seen years ago in German, but only recently discovered in English. This is the first of a series of books on modeling – it covers simple systems (integration, exponential growth and decay), logistic growth and variants, oscillations and chaos, and some interesting engineering systems (heat flow, gliders searching for thermals). These are high quality models, with units that balance, well-documented by the book. Every one I’ve tried runs in Vensim PLE so they’re great for teaching.
I haven’t had a chance to work my way through the System Zoo 2 (natural systems – climate, ecosystems, resources) and System Zoo 3 (economy, society, development), but I’m pretty confident that they’re equally interesting.
You can get the models for all three books, in English, from the Uni Kassel Center for Environmental Systems Research, http://www.usf.uni-kassel.de/cesr/. Follow the Download link and choose the Software category to obtain a .zip archive of the zoo models for the whole series, in Vensim .mdl format.
To tantalize you, here are some images of model output from Zoo 1. First, a phase map of a bistable oscillator, which was so interesting that I built one with my kids, using legos and neodymium magnets:
This is a small, discrete time model that explores the physical interpretation of the Fibonacci sequence. See my blog post about this model for details.
Fibonacci2.vpm This runs with Vensim PLE, but users might want to use the Model Reader in order to load the included .cin file with non-growing eigenvector settings.
A nifty paper on nonlinear dynamics of salmon populations caught my eye on ArXiv.org today. The math is straightforward and elegant, so I replicated the model in Vensim.
A three-species model explaining cyclic dominance of pacific salmon
Authors: Christian Guill, Barbara Drossel, Wolfram Just, Eddy Carmack
Abstract: The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various – not fully convincing – explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.
The paper does a nice job of connecting behavior to structure, and of relating the emergence of oscillations to eigenvalues in the linearized system.
Units balance, though I had to add a couple implicit scale factors to do so.
The general results are qualitatitively replicable. I haven’t tried to precisely reproduce the authors’ bifurcation diagram and other experiments, in part because I couldn’t find a precise specification of numerical methods used (time step, integration method), so I wouldn’t expect to succeed.
Unlike most SD models, this is a hybrid discrete-continuous system. Salmon, predator and zooplankton populations evolve continuously during a growing season, but with discrete transitions between seasons.
The model uses SAMPLE IF TRUE, so you need an advanced version of Vensim to run it, or the free Model Reader. (It should be possible to replace the SAMPLE IF TRUE if an enterprising person wanted a PLE version). It would also be a good candidate for an application of SHIFT IF TRUE if someone wanted to experiment with the cohort age structure.
For a more policy-oriented take on salmon, check out Andy Ford’s work on smolt migration.
This is a little experimental model that I developed to investigate stochastic allocation of rental cars. The setup for the situation is described in this thread at the Vensim forum.
There’s a single fleet of rental cars distributed around 50 cities, connected by a random distance matrix (probably not physically realizable on a 2D manifold, but good enough for test purposes). In each city, customers arrive at random, rent a car if available, and return it locally or in another city. Along the way, the dawdle a bit, so returns are essentially a 2nd order delay of rentals: a combination of transit time and idle time.
The two interesting features here are:
The interesting experiment with this model is to lower the fleet until it becomes a constraint (at around 10,000 cars).
Documentation is sparse, but units balance.
Requires an advanced Vensim version (for arrays).
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