通过屏障传播:对具有自由边界的反应扩散模型进行数值分析
Narges Shabgard1, Timothy M Schaerf1, Yihong Du1
1School of Science and Technology, University of New England, Armidale, NSW 2351, Australia.
Mathematical biosciences
|January 24, 2026
概括
这项研究从数值上分析了空间障碍如何影响入侵物种的传播. 结果显示,关键屏障的长度和严重程度决定了入侵是否被阻止或继续,而Allee效应可能有助于穿越.
科学领域:
- 数学生物学 数学生物学
- 侵袭性物种的动态 侵袭性物种的动态
- 生态建模 生态建模
背景情况:
- 了解入侵物种的传播对于生态管理至关重要.
- 之前的模型经常假设均的环境,忽视空间异质性.
- 空间障碍和环境波动可以显著影响入侵动态.
研究的目的:
- 用数值分析研究空间障碍对入侵物种传播的影响.
- 探索如何屏障长度,严重程度和时间环境波动影响入侵成功.
- 为了在Allee效应的存在和缺席下比较入侵动态.
主要方法:
- 包含空间障碍的自由边界模型的数值分析.
- 修改增长术语f (u) 以包括环境敌意 (r (x)) 和严重性 (α).
- 包含使用时间周期函数 a(t) 的时间环境波动.
- 双稳定 (艾利效应) 和单稳定 (无艾利效应) 模型之间的比较.
主要成果:
- 确定了屏障长度 (l*) 和严重程度 (α*) 的关键值,确定了入侵阻塞或延续.
- 时间环境变化的增加大小增强了入侵,而频率的增加减少了它.
- 与单稳定模型相比,Allee效应 (双稳定模型) 显示越过障碍的可能性更高.
结论:
- 空间障碍对入侵物种构成重大挑战,其长度和严重性的关键值.
- 环境的时间波动对入侵有复杂的影响,取决于规模和频率.
- 与直觉相反,Allee效应可能会促进入侵物种克服空间障碍的能力.
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