On the stability of separable solutions of a sexual age-structured population dynamics model Vladas Skakauskas * Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225 Vilnius, Lithuania Received 1 October 2002; accepted 24 May 2004 Abstract The Sharpe–Lotka–McKendrick–von Foerster equations for non-dispersing age–sex-structured popula- tions with a harmonic mean type mating law are considered and their separable solutions are analysed. For certain forms of the demographic rates the underlying evolution equations are reduced to systems of ODEs, the long time behavior of their solutions is studied, and the stability of separable solutions is discussed. It is found that for the constant death rates and constant sex ratio of newborns with stationary birth rates this model admits one one-parameter class of separable solutions, two such classes (repeated or different) or no such ones. In the case of special forms of age-dependent birth rates, solutions of one of these two different classes corresponding to the greater root of the characteristic equation are locally stable, solutions of the other one corresponding to the smaller root are unstable, and the population dies out if the model does not admit separable solutions or if initial densities of newborns are small enough in the case of the existence of separable solutions. In the case of constant vital rates, the model has no separable solutions or admits only one class of such ones that are globally stable. Ó 2004 Elsevier Inc. All rights reserved. AMS classification number: Primary 92 D 25; Secondary 35 F 25 Keywords: Population dynamics; Random mating; Age–sex-structured population 0025-5564/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.mbs.2004.05.005 * Tel.: +370 5 23 360 33; fax: +370 5 21 515 85. E-mail address: vladas.skakauskas@maf.vu.lt www.elsevier.com/locate/mbs Mathematical Biosciences 191 (2004) 41–67