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<p>A&#xa0;non-local boundary value problem is considered, describing the dynamics of the age structure in an unlimited population. A lemma on the stationary solutions of the problem is proven. Using the method of successive approximations, a&#xa0;theorem on the existence and uniqueness of a&#xa0;regular solution is established. A one-parameter family of difference schemes is constructed, and conditions for the scheme’s convergence and its stability with respect to initial data are derived. The results obtained may be useful for predicting population dynamics.</p>

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Mathematical analysis of a population model with age structure

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • M. H. Esankulova

摘要

A non-local boundary value problem is considered, describing the dynamics of the age structure in an unlimited population. A lemma on the stationary solutions of the problem is proven. Using the method of successive approximations, a theorem on the existence and uniqueness of a regular solution is established. A one-parameter family of difference schemes is constructed, and conditions for the scheme’s convergence and its stability with respect to initial data are derived. The results obtained may be useful for predicting population dynamics.