Logistic Chaos

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.

Logistic (Vensim .vpm)

Logistic (Vensim .vmf)

Ultradian Oscillations of Insulin and Glucose

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.

ultradia-enhanced-3.mdl ultradia-enhanced-3.vpm

Sea Level Rise

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