Rigorous Mapping of Data to Qualitative Properties of Parameter Values and Dynamics: A Case Study on a Two-Variable Lotka–Volterra System
Rigorous Mapping of Data to Qualitative Properties of Parameter Values and Dynamics: A Case Study on a Two-Variable Lotka–Volterra System
复制标题
数据到参数值和动态的定性属性的严格映射：二变量 Lotka–Volterra 系统的案例研究
DOI：
10.1007/s11538-023-01165-0
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发表时间：
2023
影响因子：
3.5
通讯作者：
Swigon, David
中科院分区：
文献类型：
--
作者：
Duan, Xiaoyu;Rubin, Jonathan E.;Swigon, David
在这项工作中，我们描述了主要的分析工作相关的一种新的方法来识别两个变量的Lotka-Volterra（LV）系统的参数。具体而言，这种方法是定性的，因为我们的目标不是确定模型参数的精确值，而是基于少量可用数据点建立这些参数值与它们生成的轨迹属性之间的关系。在这种情况下，我们证明了各种结果的存在性，唯一性，和符号的模型参数的系统的轨迹正好通过一组三个给定的数据点，代表最小的可能的数据集所需的模型参数值的识别。我们发现，在大多数情况下，这样的数据集确定这些值唯一的，我们也彻底调查的替代情况下，这导致非唯一性，甚至不存在的模型参数值，适合的数据。除了可识别性的结果，我们的分析提供了信息的LV系统的解决方案的长期动态直接从数据，而没有必要估计特定的参数值。
In this work, we describe mostly analytical work related to a novel approach to parameter identification for a two-variable Lotka–Volterra (LV) system. Specifically, this approach is qualitative, in that we aim not to determine precise values of model parameters but rather to establish relationships among these parameter values and properties of the trajectories that they generate, based on a small number of available data points. In this vein, we prove a variety of results about the existence, uniqueness, and signs of model parameters for which the trajectory of the system passes exactly through a set of three given data points, representing the smallest possible data set needed for identification of model parameter values. We find that in most situations such a data set determines these values uniquely; we also thoroughly investigate the alternative cases, which result in nonuniqueness or even nonexistence of model parameter values that fit the data. In addition to results about identifiability, our analysis provides information about the long-term dynamics of solutions of the LV system directly from the data without the necessity of estimating specific parameter values.