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<p>This paper studies the classical age-structured population model in an almost periodic situation. By non-densely defined operators and extended phase spaces, we define the evolution semigroups for the population model. Moreover, we define a next generation operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathscr {L}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">L</mi> </math></EquationSource> </InlineEquation> and prove that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r({\mathscr {L}})-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo stretchy="false">(</mo> <mi mathvariant="script">L</mi> <mo stretchy="false">)</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> has the same sign as the exponential growth bound of the population model. Furthermore, we investigate the asymptotic behavior of the population model via strong ergodicity. Our results extend some results of autonomous and periodic age-structured population models.</p>

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Growth Bound and Strong Ergodicity for an Almost Periodic and Age-Structured Population Model

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Jiawei Huo,
  • Shi-Ke Hu,
  • Rong Yuan

摘要

This paper studies the classical age-structured population model in an almost periodic situation. By non-densely defined operators and extended phase spaces, we define the evolution semigroups for the population model. Moreover, we define a next generation operator \({\mathscr {L}}\) L and prove that \(r({\mathscr {L}})-1\) r ( L ) - 1 has the same sign as the exponential growth bound of the population model. Furthermore, we investigate the asymptotic behavior of the population model via strong ergodicity. Our results extend some results of autonomous and periodic age-structured population models.