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<p>In this paper, we investigate population dynamics of a general competitive patch system including both diffusion and advection. We study the classification of global dynamics according to the competition coefficients <i>b</i> and <i>c</i>. Furthermore, a clear picture on the local dynamics of the two semi-trivial steady states is depicted in terms of critical competition values <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2581_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(b^*,c^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>b</mi> <mo>∗</mo> </msup> <mo>,</mo> <msup> <mi>c</mi> <mo>∗</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. Utilizing the monotone dynamical system theory, a further determination of the global dynamics in different regions on the <i>b</i>–<i>c</i> plane is presented. It is worth mentioning that during the analysis of dynamics, a significant characterization of the first eigenvalue to the linearized elliptic problem associated with our system is introduced.</p>

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Global dynamics of a Lotka–Volterra competition patch model in an advective patchy

  • 期刊论文

  • 发表日期：

    2025年8月27日

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  • Qi Wang

摘要

In this paper, we investigate population dynamics of a general competitive patch system including both diffusion and advection. We study the classification of global dynamics according to the competition coefficients b and c. Furthermore, a clear picture on the local dynamics of the two semi-trivial steady states is depicted in terms of critical competition values \(b^*,c^*\) b ∗ , c ∗ . Utilizing the monotone dynamical system theory, a further determination of the global dynamics in different regions on the b–c plane is presented. It is worth mentioning that during the analysis of dynamics, a significant characterization of the first eigenvalue to the linearized elliptic problem associated with our system is introduced.