Journal of Mathematical Biology

, Volume 28, Issue 1, pp 1–20

Dispersion population models discrete in time and continuous in space

  • D. P. Hardin
  • P. Takáč
  • G. F. Webb
Article

DOI: 10.1007/BF00171515

Cite this article as:
Hardin, D.P., Takáč, P. & Webb, G.F. J. Math. Biol. (1990) 28: 1. doi:10.1007/BF00171515

Abstract

We analyze a discrete-time model of populations that grow and disperse in separate phases. The growth phase is a nonlinear process that allows for the effects of local crowding. The dispersion phase is a linear process that distributes the population throughout its spatial habitat. Our study quantifies the issues of survival and extinction, the existence and stability of nontrivial steady states, and the comparison of various dispersion strategies. Our results show that all of these issues are tied to the global nature of various model parameters. The extreme strategies of staying-in place and going-everywhere-uniformly are compared numerically to diffusion strategies in various contexts. We approach the mathematical analysis of our model from a functional analysis and an operator theory point of view. We use recent results from the theory of positive operators in Banach lattices.

Key words

Integrodifference equation Spectral radius Dispersion 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • D. P. Hardin
    • 1
  • P. Takáč
    • 1
  • G. F. Webb
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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