捕食者-猎物相互作用的分数顺序方法:用记忆效应建模恐惧和疾病动态
Emli Rahmi1,2, Nursanti Anggriani3, Hasan S Panigoro2
1Post Doctoral Program, Department of Mathematics, Universitas Padjadjaran, Kabupaten Sumedang, Jawa Barat, Indonesia.
PloS one
|February 2, 2026
概括
这项研究引入了一种新的分数顺序捕食者-猎物模型,结合了恐惧和疾病. 它揭示了复杂的动态,包括分叉,对于理解生态系统至关重要.
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-猎物模型是生态学的基础.
- 纳入疾病和恐惧效应增加了生态动态的复杂性.
- 分数计算为模拟生物系统中的记忆效应提供了一个强大的框架.
研究的目的:
- 开发和分析一种新的分数级掠食者-猎物模型,其中包括恐惧和猎物疾病.
- 调查恐惧对猎物的招募和对受感染的猎物的选择性掠食的影响.
- 用卡普托的分数导数来探索再感染动态和记忆效应.
主要方法:
- 一个确定性的数学模型被制定和验证了存在,独特性,非负性和有限性.
- 使用马蒂尼昂条件和通用罗斯-赫尔维茨标准分析局部动力学.
- 通过利亚普诺夫函数和拉萨尔不变原理研究全球动态.
主要成果:
- 确定了三个平衡点:疾病/掠食者灭绝,没有掠食者和共存.
- 观察到Forward和Hopf的分叉,表明系统动态发生了重大变化.
- 使用预测-校正方案的数值模拟支持了分析结果.
结论:
- 恐惧和疾病的分数顺序捕食者-猎物模型表现出丰富的动态行为.
- 这项研究强调了记忆效应和恐惧在生态建模中的重要性.
- 研究结果提供了关于掠食者-猎物系统疾病传播和人口动态的见解.
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