松病控制模型的动态与非局部竞争和记忆扩散模型的动态
1College of Science, Northeast Forestry University, Harbin, Heilongjiang, 150040, PR China.
Mathematical biosciences
|September 10, 2025
概括
这项研究引入了一种新的数学模型,用于控制松病 (PWD),使用来捕食Monochamus alternatus甲虫. 该模型揭示了基于记忆的扩散如何创建复杂的空间模式,帮助PWD管理.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 森林病理学 森林病理学
背景情况:
- 松病 (PWD) 对全球森林构成重大威胁.
- 单体轮 (M. alternatus) 是PWD的主要载体.
- 木是M. alternatus的自然捕食者,因此具有生物控制的潜力.
研究的目的:
- 开发一个更现实的数学模型,用于PWD控制,包括非局部竞争和基于记忆的扩散.
- 分析拟议的M. alternatus-woodpecker模型的动态行为和分支.
- 用数学建模来解释森林疾病动态中观察到的时空异质性.
主要方法:
- 开发一种新的数学模型,模拟M. alternatus-woodpecker的相互作用.
- 对模型动态和分叉的分析,重点关注记忆扩散和非局部竞争.
- 应用常态形式理论和多个时间尺度的方法来研究霍夫分叉.
- 数字模拟使用来自中国湖北省的真实森林数据.
主要成果:
- 非本地竞争会破坏稳定的稳定状态.
- 基于记忆的扩散通过Hopf分叉诱导不稳定的,空间不均的周期溶液.
- 观察到复杂的动态行为和振荡运动,解释了生态空间时间异质性.
- 数字模拟证实了关于疾病异质性和PWD控制的理论发现.
结论:
- 拟议的模型提供了关于PWD传播动态和生物控制策略的见解.
- 基于记忆的扩散是产生疾病传播中复杂的空间模式的一个关键因素.
- 数学建模,特别是非局部和记忆效应,对于理解和管理森林生态系统和害虫至关重要.
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