放松振荡的零碎-平滑-缓慢-快速巴齐金模型与霍林格类型I功能响应
Xiao Wu1, Shuying Lu1, Feng Xie1
1College of Science, Donghua University, Shanghai 201620, China.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
这项研究分析了一个缓慢快速的Bazykinkin.
科学领域:
- 数学生物学 数学生物学
- 动态系统 动态系统
- 生态建模 生态建模
背景情况:
- 巴齐金模型是一个基本的生态模型,描述了捕食者-猎物动态.
- 研究不同时间尺度和功能反应的模型对于理解复杂的生态相互作用至关重要.
- 零碎平滑的功能反应引入了非线性,这可能导致复杂的行为.
研究的目的:
- 分析一个缓慢-快速的巴齐金模型的动态行为,结合一块-平滑的霍林格I型功能响应.
- 为了在这个特定的模型配置中识别分叉和限制周期.
- 探索诸如捕食者竞争率和初始密度等参数对模型动态的影响.
主要方法:
- 对分叉的理论分析,包括结和边界平衡分叉.
- 调查同临床和异临床循环的存在.
- 数字模拟生成相位肖像,说明不同的动态行为.
主要成果:
- 该模型显示了 Saddle-node 和 Boundary 的平衡分叉.
- 根据参数值,模型可以显示同临床周期,异临床周期或两个放松振荡周期.
- 数字模拟证实了复杂的动态,包括不同周期类型和放松振荡的共存.
结论:
- 缓慢-快速的巴齐金模型具有零碎-平滑的霍林格I型响应,比其平滑或非缓慢-快速对应物显示出明显更丰富和更复杂的动态.
- 动态行为对捕食者竞争和最初的人口密度非常敏感.
- 这些发现强调了在生态建模中考虑非光滑性和时间尺度分离的重要性.
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