Persistent age distributions for an age‐structured two‐sex population model*

An earlier version of this paper was presented at the Workshop on Nonlinear Demography, Max Planck Institute for Demographic Research, Rostock, Germany, May 26–28, 1998. The author was partially supported by a Grant‐in Aid for Scientific Research from the Japan Ministry of Education, Science and Culture. I thank Evert van Imhoff and anonymous referees for their kind suggestions.

In this paper we formulate an age‐structured two‐sex population model which takes into account a monogamous marriage rule and the duration of marriage. We are mainly concerned with the existence of exponential solutions with a persistent age distribution. First we provide a semigroup method to deal with the time‐evolution problem of our two‐sex population model. Next, by constructing a fixed point mapping, we prove the existence of exponential solutions under homogeneity conditions.

Keywords:

• Two‐Sex Population Dynamics
• Marriage Model
• Exponential Solutions
• Persistent Age Distributions
• Fixed Point Theorem
• Semigroups

Notes

An earlier version of this paper was presented at the Workshop on Nonlinear Demography, Max Planck Institute for Demographic Research, Rostock, Germany, May 26–28, 1998. The author was partially supported by a Grant‐in Aid for Scientific Research from the Japan Ministry of Education, Science and Culture. I thank Evert van Imhoff and anonymous referees for their kind suggestions.