Abstract
Mathematical models of dynamical systems often take the general form where the \(x_i\) are the variables and the \(f_i\) describe the interactions between variables. From the perspective of (3.1), the goal of science is to identify the \(x_{i}\) and the form of the functions \(f_i\).
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Notes
- 1.
This conclusion is a consequence of the second law of thermodynamics, discussed in Chapter 17.
- 2.
Archibald Vivian Hill (1886–1977), English physiologist, one of the founders of biophysics and operations research.
- 3.
Of course, if we waited a sufficiently long time, we would eventually arrive at an equilibrium state.
- 4.
Leonor Michaelis (1875–1949), German physician and biochemist. Maud Leonora Menten (1879–1960), Canadian physician and biochemist.
- 5.
George Edward Briggs (1893–1985), British botanist. John Burdon Sanderson Haldane (1892–1964), British-born Indian biologist and mathematician.
- 6.
Britton Chance (1913–2010), American biochemist.
- 7.
Bernoulli’s equations for fluid flow predict that the rate of fluid flow out of the cup will be, to a first approximation, proportional to \(\sqrt{2gh}\), where g is the acceleration due to gravity. However, we hypothesize that because of irregularities in the edge of the hole and the nonlaminar nature of water flow through the hole and from the faucet, the flow rate is more likely to be proportional to h [916]. The interested reader should perform this experiment and see whether our hypothesis is correct.
- 8.
Named for Lee Segel (1932–2005) and Marshall Slemrod (b. 1944), American applied mathematicians.
- 9.
Donald Dexter Van Slyke (1883–1971) and Glenn Ernest Cullen (1890–1940), American biochemists.
- 10.
Oliver Heaviside (1850–1925), English electrical engineer, mathematician, and physicist.
- 11.
Hans Lineweaver (1907–2009), American physical chemist, and Dean Burk (1904–1988), American biochemist.
- 12.
Michael C. Mackey (b. 1942), Canadian–American biomathematician and physiologist; Leon Glass (b. 1943), American mathematical biologist.
- 13.
André Longtin, Canadian neurophysicist (b. 1961); John Milton, (b. 1950) American–Canadian physician–scientist and mathematical biologist.
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Milton, J., Ohira, T. (2021). Equilibria and Steady States. In: Mathematics as a Laboratory Tool. Springer, Cham. https://doi.org/10.1007/978-3-030-69579-8_3
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DOI: https://doi.org/10.1007/978-3-030-69579-8_3
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