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October  2014, 19(8): 2641-2656. doi: 10.3934/dcdsb.2014.19.2641

## On a nonlinear age-structured model of semelparous species

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

Received  November 2013 Revised  April 2014 Published  August 2014

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.
Citation: Ryszard Rudnicki, Radosław Wieczorek. On a nonlinear age-structured model of semelparous species. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2641-2656. doi: 10.3934/dcdsb.2014.19.2641
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