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DENSITY-DEPENDENT LESLIE MATRIX MODELING FOR LOGISTIC POPULATIONS WITH STEADY-STATE DISTRIBUTION CONTROL
The Mathematical Scientist (2016)
  • Bruce Kessler
  • Andrew Davis
Abstract
The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity (see [1], [2], [4], [5], and [6]), with mixed results. In this paper we provide a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and the desired steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same initial population and carrying capacity, and growth rate equal to the dominant eigenvalue of the Leslie matrix minus 1.
Keywords
  • Leslie matrices; discrete population models; exponential population model; logistic population model
Publication Date
December, 2016
Citation Information
Bruce Kessler and Andrew Davis. "DENSITY-DEPENDENT LESLIE MATRIX MODELING FOR LOGISTIC POPULATIONS WITH STEADY-STATE DISTRIBUTION CONTROL" The Mathematical Scientist Vol. 41 Iss. No. 2 (December 2016) (2016) p. 119 - 128
Available at: http://works.bepress.com/bruce_kessler/91/