Don't just do something, stand there! Reflections on the counterintuitive behavior of complex systems, seen through the eyes of System Dynamics, Systems Thinking and simulation.
This is an implementation of Lorenz’ groundbreaking model that exhibits continuous-time chaos.
A google search turns up lots of good information on this model. For more advanced material, try google scholar.
I didn’t replicate this from Lorenz’ original 1963 article, Deterministic Nonperiodic Flow, but you can find a copy here.
Updated!
This is an implementation of the logistic model – a very simple example of discrete time chaotic behavior. It’s sometimes used to illustrate chaotic dynamics of insect populations.
There’s a nice description here, and the other top links on google tend to be good.
Note that this version corrects an equation error in previous versions.
Citation: Jeppe Sturis, Kenneth S. Polonsky, Erik Mokilde, and Eve van Cauter. Computer Model for Mechanisms Underlying Ultradian Oscillations of Insulin and Glucose. Am. J. Physiol. 260 (Endocrinol. Metab. 23): E801-E809, 1991.
Source: Replicated by Hank Taylor
Units: No Yes!
Format: Vensim
Ultradian Oscillations of Insulin and Glucose (Vensim .vpm)
Update, 10/2017:
Refreshed, with units defined (mathematically the same as before): ultradia2.vpm ultradia2.mdl
Further refined, for initialization in equilibrium (insulin by analytic expression; glucose by parameter). Glucose infusion turned on by default. Graphs added.
Citations: Rahmstorf 2007, “A semi-empirical approach to projecting future sea level rise.” Science 315. Grinsted, Moore & Jevrejeva 2009. “Reconstructing sea level from paleo and projected temperatures 200 to 2100 AD.” Climate Dynamics [1]
Source: Replicated by Tom Fiddaman based on an earlier replication of Rahmstorf provided by John Sterman
Units balance: Yes
Format: Vensim; requires Model Reader or an advanced version
Notes: See discussion at metasd.
Files:
Grinsted_v3b – first model; default calibration replicates Rahmstorf, and optimization is set up to adjust constant terms to fit Rahmstorf slope to data
Grinsted_v3c – second model; updated data and calibration, as in Part III
Grinsted_v3c-k2 – third model; set up for Kalman filtering, as in Part V
Illustrations of a ‘Normal’ (first order) Outflow, a Delay Outflow, and a Fixed Delay Outflow
LEARN_comparison_of_delay_n_and_delay_fixed_etc_RGD (Vensim .vmf)