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<p>From the viewpoint of mathematical analysis, we consider some crucial dynamic behaviors of time-fractional multi-species Nicholson’s blowflies system with reaction-diffusions and multiple time variable delays. In accordance to weak maximum principle of partial differential equations&#xa0;(PDEs) and time-delayed iterative technique, the existence and nonnegativity of a unique weighted pseudo <i>S</i>-asymptotically <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11498_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-time-periodic solution to the model above are addressed. Further, by utilizing the quasi-characteristic equation and fractional Halanay inequality, two types of Mittag-Leffler stability of the addressed model are obtained by the aid of a novel delay-dependent criterion on Mittag-Leffler stability for fractional-order differential equations&#xa0;(FODEs) with multiple time delays. Finally, a numerical example and its simulations are given to illustrate the effectiveness and feasibility of the conclusions in this paper. In particular, a weighted pseudo <i>S</i>-asymptotically <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11498_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-time-periodic function is designed. Our work in this paper is not only a generalization and improvement of the corresponding findings in a number of recent publications, but also establishes some theoretic and practical bases for the further researching of blowflies population dynamics.</p>

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Weighted pseudo S-asymptotic \(\omega \)-time-periodicity and Mittag-Leffler stability of time-fractional multi-species Nicholson’s blowflies model with reaction-diffusions

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Huizhen Qu,
  • Jianwen Zhou,
  • Yanning Wang

摘要

From the viewpoint of mathematical analysis, we consider some crucial dynamic behaviors of time-fractional multi-species Nicholson’s blowflies system with reaction-diffusions and multiple time variable delays. In accordance to weak maximum principle of partial differential equations (PDEs) and time-delayed iterative technique, the existence and nonnegativity of a unique weighted pseudo S-asymptotically \(\omega \) ω -time-periodic solution to the model above are addressed. Further, by utilizing the quasi-characteristic equation and fractional Halanay inequality, two types of Mittag-Leffler stability of the addressed model are obtained by the aid of a novel delay-dependent criterion on Mittag-Leffler stability for fractional-order differential equations (FODEs) with multiple time delays. Finally, a numerical example and its simulations are given to illustrate the effectiveness and feasibility of the conclusions in this paper. In particular, a weighted pseudo S-asymptotically \(\omega \) ω -time-periodic function is designed. Our work in this paper is not only a generalization and improvement of the corresponding findings in a number of recent publications, but also establishes some theoretic and practical bases for the further researching of blowflies population dynamics.