Abstract
In modern chemistry, biotechnology or ecology often the following situation has to be modeled: There is a spatially extended system consisting of a lot of individuals (or particles). These individuals may reproduce themselves or die (= “reaction”) and they are able to carry out spatial movement (= “migration”). Typical examples are chemical or microbial processes in large vessels (f.e. bioreactors or sewage treatment plants) or biological populations living in large areas.
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References
ARNOLD, L.: On the consistency of mathematical models of chemical reactions. In: Dynamics of Synergetic Systems, Springer Series in Synergetics, Vol. 6, Berlin/Heidelberg/ New York 1980.
DITTRICH, P.: A stochastic model of a chemical reaction with diffusion. Prob. Theor. Rel. Fields 79 (1988), 115–128.
FEISTEL, R., EßELING, W.: Evolution of Complex Systems, Berlin 1989.
FELSENSTEIN, J.: Excursions along the interface between disruptive selection and stabilizing selection. Genetics 93 (1979), 773–795.
HAKEN, H.: Synergetics. An Introduction. 3rd Ed., Springer, Berlin/Heidelberg/New York 1983.
ITO, K.: Distribution-valued processes arising from independent Brownian motions. Hath. Zeitschr. 182 (1983), 17–33.
JETSCHKE, G.: Hathematik der Selbstorganisation. DVW Berlin und Vieweg Braunschweig/Wiesbaden 1989.
JETSCHKE, G.: Unendlichdimensionale Diffusionsprozesse als Losungen stochastischer partieller Differentialgleichungen, Dissertation B, Jena 1989.
LANDE, R.: Genetic variation and phenotypic evolution during allopatric speciation. Amer. Natur. 116 (1980), 463–479.
HALEK-HANSOUR, H., VAN den BROECK, C., NICOLIS, G., TURNER, J.W.: Asymptotic properties of Markovian master equations, Ann. Phys. 131 (1981), 283–313.
ROUHANI, S., BARTON, R.: Speciation and the “shifting balance” in a continuous population. Theor. Popul. Biol. 31 (1987), 465–492.
VAN KAHPEN, N.G.: Stochastic processes in physics and chemistry. North-Holland, Amsterdam/New York/Oxford 1981.
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© 1991 Springer-Verlag Berlin Heidelberg
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Jetschke, G. (1991). Stochastic Modeling of Reaction-Migration Systems. In: Möller, D.P.F., Richter, O. (eds) Analyse dynamischer Systeme in Medizin, Biologie und Ökologie. Informatik-Fachberichte, vol 275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77020-3_31
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DOI: https://doi.org/10.1007/978-3-642-77020-3_31
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