阿诺德的舌头,的结构,多稳定性和生态悖论在离散时间的捕食者-猎物系统中
Rajni1, Bapan Ghosh1
1Department of Mathematics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, Madhya Pradesh, India.
Chaos (Woodbury, N.Y.)
|December 2, 2024
概括
这项研究分析了离散时间捕食者-猎物模型,揭示了混乱和多稳定性等复杂的动态. 增加猎物承载能力可能会破坏系统的稳定,影响捕食者种群,并导致灭绝风险.
科学领域:
- 生态生态学 生态生态学
- 数学生物学 数学生物学
- 动态系统 动态系统
背景情况:
- 连续时间的罗森茨瓦伊格-麦克阿瑟模型是一个基础的生态模型.
- 离散时间模型对于了解不同时间段的人口动态至关重要.
研究的目的:
- 为了研究离散时间罗森茨瓦伊格-麦克阿瑟模型的复杂动力学.
- 分析承载能力和收获对人口稳定性和行为的影响.
- 探索诸如混乱,多稳定性和分叉等现象.
主要方法:
- 利用从连续时间罗森茨瓦伊格-麦克阿瑟模型衍生出的离散时间系统.
- 在系统分析中使用零碎常数论证.
- 研究了分叉,正常形状和相位空间结构.
- 分析了收获努力的两个参数空间.
主要成果:
- 观察到各种动态行为,包括周期性,准周期性,周期翻倍,周期泡和混乱.
- 证明增加猎物承载能力可以导致稳定和不稳定.
- 识别了具有双相,三相和四相吸引子的多相稳定状态.
- 发现猎物丰富会对掠食者丰富性产生负面影响.
- 在收获参数空间中发现了阿诺德舌头和类似的结构,表明周期性加法和周期翻倍现象.
结论:
- 离散时间模型表现出其连续对应模型中不存在的丰富和复杂的动态.
- 承载能力和收获是影响人口稳定性和混乱行为的关键参数.
- 包括水效应在内的生态解释对于理解捕食掠食者捕捞策略至关重要.
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