Dynamics of a two sex population with gestation period

Giorgio Busoni; Andrzej Palczewski

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 1, page 21-34
  • ISSN: 1233-7234

Abstract

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We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent') solutions and show that such solutions exist if the model parameters satisfy two nonlinear relations.

How to cite

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Busoni, Giorgio, and Palczewski, Andrzej. "Dynamics of a two sex population with gestation period." Applicationes Mathematicae 27.1 (2000): 21-34. <http://eudml.org/doc/219257>.

@article{Busoni2000,
abstract = {We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent') solutions and show that such solutions exist if the model parameters satisfy two nonlinear relations.},
author = {Busoni, Giorgio, Palczewski, Andrzej},
journal = {Applicationes Mathematicae},
keywords = {differential equations with delay; stationary solutions; population dynamics; mathematical modelling},
language = {eng},
number = {1},
pages = {21-34},
title = {Dynamics of a two sex population with gestation period},
url = {http://eudml.org/doc/219257},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Busoni, Giorgio
AU - Palczewski, Andrzej
TI - Dynamics of a two sex population with gestation period
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 1
SP - 21
EP - 34
AB - We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent') solutions and show that such solutions exist if the model parameters satisfy two nonlinear relations.
LA - eng
KW - differential equations with delay; stationary solutions; population dynamics; mathematical modelling
UR - http://eudml.org/doc/219257
ER -

References

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  1. [1] G. Busoni and S. Matucci, Population dynamics with delay, Studi Urbinati I (1997), 119-137 (paper presented at the meeting 'La matematica nei problemi dell'ambiente, della biologia e della medicina', Urbino, 1996). 
  2. [2] K. P. Hadeler, Pair formation models with maturation period, J. Math. Biology 32 (1993), 1-15. Zbl0808.92024
  3. [3] L. Teglielli, Dinamica di popolazioni a due sessi, Ricerca di soluzioni per sistenti, Università di Firenze, 1998. 

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