在Beddington-DeAngelis捕食者-猎物模型中进行分叉分析,其中包括息地复杂性和额外的食物效应
Demou Luo1,2, Qiru Wang3, Huayou Xie1
1School of Mathematics, Sun Yat-sen University, Guangzhou 510275, Guangdong, People's Republic of China.
Chaos (Woodbury, N.Y.)
|July 21, 2025
概括
这项研究分析了捕食者-猎物模型,揭示了受息地和食物可用性影响的复杂动态. 该研究详细介绍了各种分叉现象和新出现的行为,如多个共存状态.
科学领域:
- 数学生物学 数学生物学
- 生态生态学 生态生态学
- 动态系统理论 动态系统理论
背景情况:
- 捕食者-猎物模型在生态学中对于理解人口动态至关重要.
- 与更简单的模型相比,贝丁顿-德安吉利斯功能反应提供了更现实的捕食者食行为的描述.
- 息地复杂性和额外的食物来源是影响物种相互作用的关键环境因素.
研究的目的:
- 为了研究捕食者-猎物模型的复杂动态,结合Beddington-DeAngelis功能反应.
- 分析息地复杂性和额外的食物对掠食者-猎物系统稳定性和行为的影响.
- 在模型中识别和描述分叉现象和新出现的动态状态.
主要方法:
- 利用基于微分方程的数学模型来表示捕食者-猎物相互作用.
- 应用了分叉理论来系统地分析系统动态中的关键过渡.
- 采用数值模拟来验证分析结果,并说明复杂的行为.
主要成果:
- 识别了多个分叉现象,包括Hopf,结,跨临界,以及一个共维两型的Bogdanov-Takens分叉.
- 证明了各种动态的出现,如同临床轨道和多个共存的周期和稳定状态.
- 确认息地复杂性和额外的食物对系统的稳定性和可能的结果的影响很大.
结论:
- 具有贝丁顿-德安吉利斯反应的捕食者-猎物模型表现出丰富而复杂的动态.
- 像息地复杂性和食物供应等环境因素在塑造生态相互作用和系统稳定性方面发挥着关键作用.
- 这项研究为理解生态相关情景中的复杂人口动态提供了理论框架.
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