Logistic Map& Bifurcation diagram: Searching for some examples in nature

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Offline Fraktalist

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« on: July 31, 2019, 01:19:58 PM »
I'm doing a first talk on fractals in a month and am searching for good examples where the logistic map can be used to model things in nature/cosmos.
Obligatory animal populations. But does anyone know any others?
Also happy to learn any interesting facts about the logistic map if you want to share.

Cheers,
Fraktalist

Offline claude

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« Reply #1 on: July 31, 2019, 02:09:49 PM »
Not the logistic map, but physical models of dripping taps / faucets exhibit chaos and have their own bifurcation diagrams. It's interesting due to the discrete drips while the model is otherwise continuous.

Offline ThunderboltPagoda

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« Reply #2 on: August 12, 2019, 12:45:17 AM »
I'm doing a first talk on fractals in a month and am searching for good examples where the logistic map can be used to model things in nature/cosmos.
Obligatory animal populations. But does anyone know any others?

You can find the logistic map in cell metabolism, for instance in enzyme kinetics. The German-Chilean physicist Mario Markus had researched with his colleagues the kinetics of glycolysis in yeast cells, which led him to invent the Lyapunov fractals.

Here are some of his papers:

M. Markus and B. Hess, "Transitions between oscillatory modes in a glycolytic model system", Proc. Natl. Acad. Sciences USA 81, 4394-4398 (1984)
M. Markus, D. Kuschmitz and B. Hess, "Chaotic dynamics in yeast glycolysis under periodic substrate input flux", FEBS Lett. 172, 235-238 (1984)
M. Markus, S.C. Mueller and B. Hess "Observation of Entrainment, Quasiperiodicity and Chaos in Glycolyzing Yeast Extracts under Periodic Glucose Input", Ber. Bunsenges. Phys. Chem. 89, 651-654 (1985)
M. Markus, D. Kuschmitz and B. Hess, "Properties of strange attractors in yeast glycolysis", Biophysical Chemistry 22, 95-105 (1985)
M. Markus and B. Hess, "Order and chaos in biochemistry", Trends in Biochemical Sciences 12, 45-48 (1987)
M. Markus and B. Hess, "Lyapunov exponents of the logistic map with periodic forcing", Computer and Graphics 13, 553-558 (1989)

Offline ThunderboltPagoda

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« Reply #3 on: August 12, 2019, 04:11:51 PM »
Here is an early account from Scientific American:

http://www.mariomarkus.com/reports/reports_B2.html

Offline Adam Majewski

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« Reply #4 on: August 12, 2019, 05:18:42 PM »

May, Robert M. (1976). "Simple mathematical models with very complicated dynamics". Nature. 261 (5560): 459467. Bibcode:1976Natur.261..459M. doi:10.1038/261459a0.

Offline Fraktalist

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« Reply #5 on: August 12, 2019, 08:45:06 PM »
Thanks guys!!  :thumbs:


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