Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-13 DOI:10.1088/1751-8121/ad6ab2
Fabián Aguirre-López
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Abstract

We study the dynamics of the generalized Lotka–Volterra model with a network structure. Performing a high connectivity expansion for graphs, we write down a mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe the fixed points of the model in terms of a few simple order parameters. We extend the analysis even for diverging abundances, using a mapping to the replicator model. With this we present a unified approach for both cooperative and competitive systems that display complementary behaviors. In particular we show the central role of an order parameter called the critical degree, gc. In the competitive regime gc serves to distinguish high degree nodes that are more likely to go extinct, while in the cooperative regime it has the reverse role, it will determine the low degree nodes that tend to go relatively extinct.
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网络上广义洛特卡-伏特拉模型的异质均场分析
我们研究了具有网络结构的广义 Lotka-Volterra 模型的动力学。通过对图形进行高连接性扩展,我们写出了包含度异质性的均场动力学理论。这样,我们就能用几个简单的阶次参数来描述模型的定点。我们利用复制器模型的映射,扩展了对发散丰度的分析。这样,我们就为显示互补行为的合作和竞争系统提供了一种统一的方法。我们特别展示了一个称为临界度 gc 的阶次参数的核心作用。在竞争系统中,临界值 gc 的作用是区分更有可能消亡的高程度节点,而在合作系统中,它的作用正好相反,它将决定倾向于相对消亡的低程度节点。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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