Abstract
We now have to make a detour out of mathematics into science. We have to ask, what are the fundamental kinds of behaviors that can be seen in a scientific system, and what do they look like mathematically?
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Notes
- 1.
Some sources refer to all closed trajectories as “limit cycles.” On the other hand, a few reserve the term for stable closed trajectories.
- 2.
In ecology, the same function is sometimes called the “Holling Type III function” and is used to model the feeding behavior of vertebrates.
- 3.
Mathematically, this function is called a rectangular hyperbola, but it goes by several other names in biology, including the “Holling Type II functional response” in ecology and “Michaelis–Menten kinetics” in biochemistry.
- 4.
Farkas et al. (2002) refers to a stadium wave as “La Ola,” Spanish for “wave.” They report that the first recorded stadium wave was at Azteca stadium in Mexico City during the 1986 World Cup. Their paper uses an excitable medium model of the stadium wave.
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Garfinkel, A., Shevtsov, J., Guo, Y. (2017). Nonequilibrium Dynamics: Oscillation. In: Modeling Life. Springer, Cham. https://doi.org/10.1007/978-3-319-59731-7_4
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DOI: https://doi.org/10.1007/978-3-319-59731-7_4
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