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<p>Both stochasticity and seasonality are crucial natural factors that prominently influence real ecosystems. Counterintuitive phenomena, which are absent in deterministic models, can be induced by noise. In this study, we investigate stochastic bifurcation and periodic solutions in two stochastic single-species models that incorporate the Allee effect and aposematism, aiming to elaborate on these phenomena. Our findings show that the critical threshold parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1353_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> determines not only the persistence and extinction of species but also the D-bifurcation and P-bifurcation of the system. Additionally, noise, predation, and aposematism can all trigger P-bifurcation, but with varying numbers of bifurcations. Ecologically speaking, both noise and predation harm population survival, whereas aposematic behavior serves as an effective defense mechanism against predation, rather than contributing to population decline.</p>

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Stochastic Bifurcation and Periodic Solution in Stochastic Single-Species Models Incorporating Allee Effect and Aposematism

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Xingwang Yu,
  • Tiantian Liu,
  • Yuanlin Ma

摘要

Both stochasticity and seasonality are crucial natural factors that prominently influence real ecosystems. Counterintuitive phenomena, which are absent in deterministic models, can be induced by noise. In this study, we investigate stochastic bifurcation and periodic solutions in two stochastic single-species models that incorporate the Allee effect and aposematism, aiming to elaborate on these phenomena. Our findings show that the critical threshold parameter \(\Lambda \) Λ determines not only the persistence and extinction of species but also the D-bifurcation and P-bifurcation of the system. Additionally, noise, predation, and aposematism can all trigger P-bifurcation, but with varying numbers of bifurcations. Ecologically speaking, both noise and predation harm population survival, whereas aposematic behavior serves as an effective defense mechanism against predation, rather than contributing to population decline.