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在平面捕食者-猎物系统中,单一的Hopf分叉的进一步稳定性标准
Jicai Huang1, Shimin Li2, Xiaoling Wang3
1School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China.
Chaos (Woodbury, N.Y.)
|May 22, 2025
概括
这项研究分析了捕食者-猎物模型中的奇异的Hopf分叉稳定性,特别是当Lyapunov系数为零时. 对莱斯利和高斯模型建立了新的标准,并通过数值模拟证实了这一点.
科学领域:
- 数学生物学 数学生物学
- 动态系统理论 动态系统理论
- 生态生态学 生态生态学
背景情况:
- 在分析捕食者-猎物系统时,单点Hopf分叉是至关重要的.
- 现有的研究为分叉 (A≠0) 提供了利亚普诺夫系数,但当A=0.0时,稳定性不清楚.
- 平面捕食者-猎物系统是基本的生态模型.
研究的目的:
- 在平面捕食者-猎物系统中,当第一个Lyapunov系数为零 (A=0) 时,研究单一的Hopf分叉的稳定性.
- 为这个特定的分叉案例推导并提出新的稳定性标准.
- 扩大对超临界 (A<0) 和亚临界 (A>0) 分叉的理解,超出现有结果.
主要方法:
- 在霍夫分叉的背景下对单一扰动理论的分析.
- 对于平面捕食者-猎物模型的稳定性标准的推导.
- 方法应用于莱斯利和高斯类型的掠食者-猎物系统.
- 数字模拟用于验证分析结果.
主要成果:
- 在平面捕食者-猎物系统中,在A=0处单一的Hopf分叉建立了新的稳定性标准.
- 该分析专门针对A=0案例的知识差距.
- 数字模拟证实了衍生的分析稳定性标准.
结论:
- 这项工作为捕食者-猎物系统中独特的Hopf分叉稳定性提供了全面的理解,特别是在以前未解决的A=0场景中.
- 这些发现有助于生态建模和动态系统的理论框架.
- 经过验证的标准增强了捕食者-猎物模型的预测能力.
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