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论文中文题名：

 <font color='red'></font>对<font color='red'></font>流<font color='red'></font>环<font color='red'></font>境<font color='red'></font>中<font color='red'></font>一<font color='red'></font>类<font color='red'></font>捕<font color='red'></font>食<font color='red'></font>-<font color='red'></font>食<font color='red'></font>饵<font color='red'></font>模<font color='red'></font>型<font color='red'></font>的<font color='red'></font>动<font color='red'></font>力<font color='red'></font>学<font color='red'></font>研<font color='red'></font>究<font color='red'></font>    

姓名：

 冯花    

学号：

 <font color='red'></font>2<font color='red'></font>2<font color='red'></font>2<font color='red'></font>0<font color='red'></font>1<font color='red'></font>0<font color='red'></font>0<font color='red'></font>9<font color='red'></font>0<font color='red'></font>0<font color='red'></font>1<font color='red'></font>    

保密级别：

 <font color='red'></font>公<font color='red'></font>开<font color='red'></font>    

论文语种：

 <font color='red'></font>c<font color='red'></font>h<font color='red'></font>i<font color='red'></font>    

学科代码：

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学科名称：

 <font color='red'></font>理<font color='red'></font>学<font color='red'></font> <font color='red'></font>-<font color='red'></font> <font color='red'></font>数<font color='red'></font>学<font color='red'></font> <font color='red'></font>-<font color='red'></font> <font color='red'></font>基<font color='red'></font>础<font color='red'></font>数<font color='red'></font>学<font color='red'></font>    

学生类型：

 <font color='red'></font>硕<font color='red'></font>士<font color='red'></font>    

学位级别：

 <font color='red'></font>理<font color='red'></font>学<font color='red'></font>硕<font color='red'></font>士<font color='red'></font>    

学位年度：

 <font color='red'></font>2<font color='red'></font>0<font color='red'></font>2<font color='red'></font>5<font color='red'></font>    

培养单位：

 <font color='red'></font>西<font color='red'></font>安<font color='red'></font>科<font color='red'></font>技<font color='red'></font>大<font color='red'></font>学<font color='red'></font>    

院系：

 理学院    

专业：

 数学    

研究方向：

 <font color='red'></font>反<font color='red'></font>应<font color='red'></font>扩<font color='red'></font>散<font color='red'></font>方<font color='red'></font>程<font color='red'></font>    

第一导师姓名：

 王彪    

第一导师单位：

 西安科技大学    

论文提交日期：

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论文答辩日期：

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论文外文题名：

 <font color='red'></font>D<font color='red'></font>y<font color='red'></font>n<font color='red'></font>a<font color='red'></font>m<font color='red'></font>i<font color='red'></font>c<font color='red'></font> <font color='red'></font>A<font color='red'></font>n<font color='red'></font>a<font color='red'></font>l<font color='red'></font>y<font color='red'></font>s<font color='red'></font>i<font color='red'></font>s<font color='red'></font> <font color='red'></font>o<font color='red'></font>f<font color='red'></font> <font color='red'></font>a<font color='red'></font> <font color='red'></font>C<font color='red'></font>l<font color='red'></font>a<font color='red'></font>s<font color='red'></font>s<font color='red'></font> <font color='red'></font>o<font color='red'></font>f<font color='red'></font> <font color='red'></font>P<font color='red'></font>r<font color='red'></font>e<font color='red'></font>d<font color='red'></font>a<font color='red'></font>t<font color='red'></font>o<font color='red'></font>r<font color='red'></font>-<font color='red'></font>p<font color='red'></font>r<font color='red'></font>e<font color='red'></font>y<font color='red'></font> <font color='red'></font>M<font color='red'></font>o<font color='red'></font>d<font color='red'></font>e<font color='red'></font>l<font color='red'></font>s<font color='red'></font> <font color='red'></font>i<font color='red'></font>n<font color='red'></font> <font color='red'></font>A<font color='red'></font>d<font color='red'></font>v<font color='red'></font>e<font color='red'></font>t<font color='red'></font>i<font color='red'></font>v<font color='red'></font>e<font color='red'></font> <font color='red'></font>E<font color='red'></font>n<font color='red'></font>v<font color='red'></font>i<font color='red'></font>r<font color='red'></font>o<font color='red'></font>n<font color='red'></font>m<font color='red'></font>e<font color='red'></font>n<font color='red'></font>t<font color='red'></font>s<font color='red'></font>    

论文中文关键词：

 捕食-食饵模型 ; 对流环境 ; 稳定性 ; 存在性    

论文外文关键词：

 Predator-prey model ; Advective environment ; Stability ; Existence    

论文中文摘要：

全球气候变化与人类活动加剧了对流环境对生态系统的调控作用，传统Lotka-Volterra模型因忽略流体输运与边界效应，难以解析动态迁移环境中的物种互作机制。本研究聚焦于对流环境，构建了一类捕食-食饵反应-扩散-对流耦合模型，其中食饵在空间异质性环境中形成稳定分布，其密度随对流强度增加而向河流下游偏移，因此在上游端施加Neumann边界条件；通过调节下游流失强度，可量化人类活动对生态系统的干预效应，因此下游端施加Robin边界条件，增强了模型的生态真实性。

首先研究了对流环境中捕食-食饵模型半平凡解依赖于捕食者扩散速率的稳定性。通过构建反应-扩散-对流耦合系统，结合异质性资源分布与Holling II型功能响应函数。采用变分原理与特征值分析，结合Krein-Rutman定理与椭圆正则性理论，建立了主特征值与稳定性关系的普适框架，并通过下游流失强度参数 分析揭示了环境对流对物种生存阈值的调控规律。研究结果表明，当 时，被捕食者扩散速率以及对流速率需要大于一个常数，捕食者能否入侵取决于其扩散速率和死亡率的阈值组合：当捕食者的死亡率很小时，对于任意的捕食者扩散速率，该半平凡解是不稳定的；当捕食者的死亡率处于某个中间区域时，随着捕食者扩散速率增由小变大，半平凡解的稳定性由不稳定改变为渐近稳定；当捕食者的死亡率很大时，对于任意的捕食者扩散速率，该半平凡解都是渐近稳定的；对于 ，捕食者需更低扩散率才能入侵。高死亡率下稳定性不受扩散速率影响，半平凡解是渐近稳定的。

根据上述关于半平凡解稳定性的完整刻画，进一步研究对流环境中捕食-食饵模型正稳态解的存在性和稳定性。根据局部分歧理论与椭圆正则性分析，以捕食者扩散系数 为分歧参数，并通过参数 进行分析。研究结果表明：当 时，正稳态解通过次临界分岔从半平凡解 产生，而当 时，下游强流失效应导致分岔方向反转为超临界分岔，需更低扩散率才能维持共存。线性稳定性分析表明，分岔产生的正稳态解是渐近稳定的。

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论文外文摘要：

Global climate change and intensified human activities have amplified the regulatory effects of advective environments on ecosystems. Traditional Lotka-Volterra models, which neglect fluid transport and boundary effects, demonstrate limitations in analyzing species interaction mechanisms within dynamic migration environments. This study focuses on advective environments to establish a novel predator-prey reaction-diffusion-advection coupling model. The model features prey species forming stable distributions in spatially heterogeneous environments, with their density exhibiting downstream shifts along river systems as advection intensity increases. Consequently, Neumann boundary conditions are implemented at the upstream end to reflect this spatial pattern. Through modulation of downstream loss intensity, the model quantitatively evaluates anthropogenic interventions in ecosystems, with Robin boundary conditions applied at the downstream end to enhance ecological realism. This configuration effectively integrates hydrodynamic transport processes with biological interactions, providing a robust framework for analyzing ecosystem responses to coupled environmental and anthropogenic stressors.

This study first investigates the stability of semi-trivial solutions in advective predator-prey models dependent on predator diffusion rates. By constructing a reaction-diffusion-advection coupled system incorporating heterogeneous resource distributions and the Holling type II functional response, we establish a universal framework linking principal eigenvalues to stability through variational principles, eigenvalue analysis, the Krein-Rutman theorem, and elliptic regularity theory. Analysis of parameter  elucidates the regulatory mechanisms of environmental advection on species survival thresholds. The results demonstrate that when , both the prey diffusion rate and advection rate must exceed specific constants, and the predator’s invasion capability depends on threshold combinations of its diffusion rate and mortality. When the predator’s mortality rate is extremely small, the semi-trivial solution remains unstable under any predator diffusion rate; when the mortality rate lies within an intermediate range, the stability of the semi-trivial solution transitions from unstable to asymptotically stable as the predator diffusion rate increases; and when the mortality rate is sufficiently large, the semi-trivial solution maintains asymptotic stability regardless of the predator’s diffusion rate. For , predators require lower diffusion rates to invade successfully. Under high mortality rates, stability becomes independent of diffusion effects, ensuring persistent asymptotic stability of the semi-trivial solution.

Based on the comprehensive characterization of semi-trivial solution stability, this study further investigates the existence and stability of positive steady-state solutions in advective predator-prey models. By employing local bifurcation theory and elliptic regularity analysis with the predator diffusion coefficient  as the bifurcation parameter and incorporating parameter , the results reveal that when , positive steady-state solutions emerge from the semi-trivial solution  via subcritical bifurcation, whereas under , the strong downstream loss effect inverts the bifurcation direction to supercritical bifurcation, necessitating lower diffusion rates to sustain species coexistence. Linear stability analysis confirms the asymptotic stability of bifurcated positive steady-state solutions.

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