Patterns of Population Growth and Dispersal

  • Frank C. Hoppensteadt
  • Charles S. Peskin
Part of the Texts in Applied Mathematics book series (TAM, volume 10)


Bacteria in our gut, insects in a field, trees in a forest, and plants borne by air and water around the world are among the many examples of spatial distributions of organisms that are important and interesting to study. Mechanisms of pattern formation and dispersal operate on a wide range of spatial scales from microscopic random movements to long-distance transport by air or water. On the other hand, organisms can also reflect uneven distributions of nutrients or toxins in their growth patterns. These are important, for example, in palenology, where the distributions of microbial fossils are used to find oil, and they provide places to look for new species of microbes, such as petroleum-digesting bacteria that are now used to clean oil tanks.


Markov Chain Random Walk Diffusion Equation Periodic Boundary Condition Sample Path 
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Annotated References

  1. Mourant, A.E., Kopec, A.C., and Domaniewicz-Sobczak, K.: The Distribution of Blood Groups and Other Polymorphisms, 2nd ed. Oxford Univ. Press, New York, 1976.Google Scholar
  2. Murray, J.D.: Mathematical Biology, Springer-Verlag, New York, 1989.CrossRefzbMATHGoogle Scholar
  3. Hoppensteadt, F.C.: Mathematical Methods in Population Biology, Cambridge University Press, Cambridge, 1982.CrossRefzbMATHGoogle Scholar
  4. Oksendal, Br.Stochastic Differential Equations, Springer-Verlag, New York, 1992.CrossRefGoogle Scholar
  5. Einstein, A.: Investigation on the Theory of Brownian Movement, Dover Publics., New York, 1956.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  • Charles S. Peskin
    • 2
  1. 1.Center for Systems Science and EngineeringArizona State UniversityTempeUSA
  2. 2.Department of Mathematics Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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