论文标题
密度依赖性扩散对避难所模式形成的影响
Influence of density-dependent diffusion on pattern formation in a refuge
论文作者
论文摘要
我们研究了Fisher-KPP方程的非局部概括，该方程融合了物种种群在可行的斑块中（避难）。在此框架中，扩散起着同质性的作用，而非局部相互作用会破坏空间均匀状态的稳定，从而导致自发模式的出现。值得注意的是，即使统一状态稳定，避难所的存在，例如存在的空间扰动仍然可以诱导模式。这些现象以具有恒定扩散率的环境而闻名。我们的目标是研究当扩散率依赖于密度时，人口分布中眨眼的形成如何受到影响。然后，我们探索场景，其中扩散率对稀疏或人满为患敏感。我们发现，国家依赖性扩散率会影响模式的形状和稳定性，这可能导致人口分布的爆炸性生长或破碎，这取决于扩散对密度变化的反应。
We investigate a nonlocal generalization of the Fisher-KPP equation, which incorporates logistic growth and diffusion, for a single species population in a viable patch (refuge). In this framework, diffusion plays an homogenizing role, while nonlocal interactions can destabilize the spatially uniform state, leading to the emergence of spontaneous patterns. Notably, even when the uniform state is stable, spatial perturbations, such as the presence of a refuge, can still induce patterns. These phenomena are well known for environments with constant diffusivity. Our goal is to investigate how the formation of winkles in the population distribution is affected when the diffusivity is density-dependent. Then, we explore scenarios in which diffusivity is sensitive to either rarefaction or overcrowding. We find that state-dependent diffusivity affects the shape and stability of the patterns, potentially leading to either explosive growth or fragmentation of the population distribution, depending on how diffusion reacts to changes in density.
