On a nonlinear age-structured model of  semelparous species

Ryszard Rudnicki; Radosław Wieczorek

doi:10.3934/dcdsb.2014.19.2641

Article Contents

2014, Volume 19, Issue 8: 2641-2656. Doi: 10.3934/dcdsb.2014.19.2641

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On a nonlinear age-structured model of semelparous species

Ryszard Rudnicki^1, and
Radosław Wieczorek^2,

1.
Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice
2.
Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice

Received: October 31, 2013

Revised: March 31, 2014

Published: September 2014

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Abstract

We study a nonlinear age-structured model of a population such that individuals may give birth only at a given age. Properties of measure-valued periodic solutions of this system are investigated. We show that in some cases the age profile of the population tends to a Dirac measure, which means that the population asymptotically consists of individuals at the same age. This phenomenon is observed in nature in some insects populations.

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Mathematics Subject Classification: Primary: 92D25; Secondary: 35F20, 45G10.

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