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卡普托等级的动态分析异常顺序的分数微分系统与双倍的时间延迟
Wangwang Liu1, Xiaolin Lin1, Danfeng Pang1
1School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021, People's Republic of China.
这项研究引入了一种新的分数捕食者-猎物模型,其中包括食人主义和恐惧,并考虑了不同物种的记忆效应和时间延迟. 该研究分析了稳定性和分叉,通过数值模拟验证发现.
科学领域:
- 数学生物学 数学生物学
- 生态生态学 生态生态学
- 分数微积分的计算.
背景情况:
- 捕食者-猎物模型对于理解生态动态至关重要.
- 分数计算为模拟生物系统中的记忆效应提供了一种更细致的方法.
- 现有的模型往往简化了物种的记忆和延迟动态.
研究的目的:
- 开发和分析卡普托的异性顺序分数捕食者-猎物模型.
- 将食人主义,恐惧效应和双重时间延迟纳入其中.
- 调查异质记忆和时间延迟对系统稳定性和动态的影响.
主要方法:
- 卡普托构建了一个异性顺序的分数捕食者-猎物系统.
- 对系统独特性,边界性和平衡点存在的分析.
- 应用分叉理论来研究霍夫分叉与恐惧,食人主义和时间延迟有关.
- 数字模拟用于验证.
主要成果:
- 为正平衡点的存在和稳定性而建立的条件.
- 鉴定了受食人,恐惧和时间延迟影响的霍夫分叉现象.
- 证明模型能够捕捉来自异质记忆和延迟的复杂动态.
- 通过数值模拟验证了理论发现.
结论:
- 开发的分数模型提供了更现实的捕食者-猎物相互作用的表示.
- 异质的记忆效应和时间延迟显著影响生态系统的稳定性.
- 这项研究提供了关于恐惧和食人群的复杂动态的见解.
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