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de Gregorio, S.; Pielke, R. A.; Dalu, G. A.

Feedback between a simple biosystem and the temperature of the Earth. (English) Zbl 0790.92024

J. Nonlinear Sci. 2, No. 3, 263-292 (1992).
Summary: A detailed mathematical analysis is presented of the model of Daisyworld, proposed by A. J. Watson and J. Lovelock [Tellus, 35 B, 284- 289 (1983)]. The stationary solutions of a resulting quartic system of ODEs are examined and their local and global attractivity is proved. The model shows, in a suitable range of values of the albedo and of the diffusion of the temperature, a mitigation of the climate in response to luminosity perturbations. The feedback between the biological components and the Earth’s climate can be so efficient that the temperature of the Earth will stay practically constant even under substantial variations of the solar luminosity.

Cited in 4 Documents

MSC:

92D40 Ecology
86A10 Meteorology and atmospheric physics
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D99 Genetics and population dynamics
34D05 Asymptotic properties of solutions to ordinary differential equations

Keywords:

biosystem behavior; Earth temperature; diffusion of temperature; periodic and linear variation of luminosity; asymptotic local and global stability; model of Daisyworld; stationary solutions; quartic system of ODEs; local and global attractivity; luminosity perturbations; Earth’s climate; solar luminosity
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References:

[1] Cotton, W. R., and R. A. Pielke, 1992: Human impacts on weather and climate.Geophys. Sci. Ser. Vol II. Aster Press, in press.
[2] Isakari, S. M., and R. C. Sommerville (1989): Accurate numerical solutions for Daisy world.Tellus,41B, 478-82. · doi:10.1111/j.1600-0889.1989.tb00324.x
[3] Watson, A. J., and J. Lovelock (1982): The regulation of carbon dioxide and climate. Gaia or geochemistry?Planet. Space Sci.,30, 793-802.
[4] Watson, A. J., and J. Lovelock (1983): Biological homeostasis of the global environment: the parable of Daisyworld.Tellus,35B, 284-289. · doi:10.1111/j.1600-0889.1983.tb00031.x
[5] Zeng, X., R. A. Pielke, and R. Eykholt, 1990: Chaos in Daisyworld.Tellus,42B, 309-318.
[6] Zeng, X., R. A. Pielke, and R. Eykholt, 1992: Reply to Jascourt and Raymond.Tellus,42B, in press.
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