一个缓慢-快速的莱斯利-高尔捕食者-猎物模型的动力学与猎物收获
Yantao Yang1,2, Xiang Zhang3, Jian Zu1
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
Chaos (Woodbury, N.Y.)
|October 7, 2024
概括
这项研究探讨了莱斯利-高尔捕食者-猎物模型,揭示了复杂的全球动态和新的现象,如鸟爆炸和多个稳定状态的共存. 数字模拟验证了这些发现.
科学领域:
- 数学生物学 数学生物学
- 生态生态学 生态生态学
- 动态系统理论 动态系统理论
背景情况:
- 莱斯利-高尔捕食者-猎物模型是一个基本的生态模型.
- 之前的研究重点是局部分叉和特定的循环特性.
- 这个模型的缓慢-快速动态在很大程度上仍未被探索.
研究的目的:
- 为了研究莱斯利-高尔捕食者-猎物模型的全球动态,在缓慢-快速的环境中采集迈凯利斯-门的猎物.
- 为了发现已知的局部分叉之外的更丰富的动态现象.
- 识别和描述新的动态行为,包括潜在的新现象.
主要方法:
- 慢速捕食者-猎物模型的分析.
- 全球动态和分叉的研究.
- 使用理论分析和数值模拟.
主要成果:
- 确定一个平衡点的全球稳定性.
- 观察到一个不稳定的canard循环爆炸成一个同临床循环.
- 发现了稳定和不稳定的卡纳德周期的共存,导致具有不同特征的卡纳德爆炸.
- 报告了一种新的放松振荡与短胡子,一个潜在的新动态现象.
结论:
- 缓慢快速的设置揭示了莱斯利-高尔模型中比以前知道的更丰富的全球动态.
- 已经确定了新的现象,包括复杂的canard爆炸和一种新的放松振荡.
- 数字模拟证实了这些复杂的动态行为的存在和特征.
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