Mackey-Glass Equation

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This Demonstration shows solutions of the Mackey–Glass equation for the density, , of mature circulating white blood cells. The parameter is the delay between production and maturation and release into the bloodstream of the cells.

Contributed by: Rob Knapp (March 2011)
Open content licensed under CC BY-NC-SA



The first half of the solution is shown in gray so that you can see how transients decay. The values of , and are constant and chosen to be the same as those shown in figure 2 of [1].

[1] M. C. Mackey and L. Glass, "Oscillation and Chaos in Physiological Control Systems," Science, 197, pp. 287–289.

Snapshot 1: with reproduces figure 2(b) in [1]

Snapshot 2: with reproduces figure 2(c) in [1]

Snapshot 3: the same value of as snapshot 2 in the delay plane

Snapshot 4: shows a very chaotic solution with

Snapshot 5: there is an attractive fixed point with

Snapshot 6: there is a limit cycle with

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