通过比例-差异控制稳定鱼-藻类结合地图格子模型的时空动态
Yanhua Zhu1, Xiangyi Ma1, Jinliang Wang1
1Department of Mathematics, Beihang University, Changping, Beijing, 100191, People's Republic of China.
Journal of mathematical biology
|October 6, 2025
概括
这项研究使用合地图格子 (CMLs) 建模了-藻 (M-A) 系统. 比例差分 (PD) 控制通过防止混乱动态和确保统一分布来稳定藻类种群,这对海洋水产养殖生态系统至关重要.
科学领域:
- 海洋生态海洋生态学
- 数学生物学 数学生物学
- 水产养殖系统 水产养殖系统
背景情况:
- 藻 (M-A) 系统对于海洋水产养殖生态系统平衡至关重要.
- 藻类种群动态显著影响的生长和繁殖,反之亦然.
- 了解M-A系统动态是保持水产养殖稳定的关键.
研究的目的:
- 为MA系统开发一个空间时间分离的合地图格子 (CMLs) 模型.
- 在MA系统模型中分析稳定性和分叉 (翻转和图灵).
- 调查比例差分 (PD) 控制对MA系统动态和稳定性的影响.
主要方法:
- 结合地图格子 (CMLs) 建模,包括自我扩散和交叉扩散.
- 线性稳定性分析和分叉理论用于分类固定点和确定分叉条件.
- 数字模拟以探索时间动态,时空模式和PD控制的影响.
主要成果:
- CMLs模型揭示了丰富的时间动态和来自五种不同的机制的时空模式.
- 引入了PD控制,成功地延迟了翻转分叉,并防止了藻类密度中的多周期振荡和混乱.
- 控制PD减少了图灵不稳定区域,并调节了图灵模式类型,促进了藻类的均分布.
结论:
- 开发的CMLs模型提供了对M-A系统动态和稳定性的洞察.
- 控制PD是一种有效的策略,可以稳定藻类种群,防止M-A系统中的生态系统不稳定.
- 这项研究通过先进的建模和控制策略,有助于保持稳定和生产力的海洋水产养殖生态系统.
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