无序动力系统中的广义相关性:来自多物种Lotka-Volterra模型的见解。

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Sebastian H Castedo, Joshua Holmes, Joseph W Baron, Tobias Galla
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引用次数: 0

摘要

在无序系统的研究中,人们经常选择一个独立的同分布相互作用系数矩阵来表示组件之间的猝灭随机耦合,可能具有一些对称约束或对角线相反的元素对之间的相关性。然而,一组更通用的耦合仍然保留了组件的统计互换性,可能涉及仅共享单个行或列索引的交互系数之间的相关性。这些相关性已被证明在诸如广义Lotka-Volterra方程(gLVEs)之类的系统中自然出现。在这项工作中,我们进行了动态平均场分析,以了解单指数相关性如何影响无序系统的动力学和稳定性,并以glve为例。我们表明,即使在相互作用系数的总体方差保持不变的情况下,行相关性也会提高平均场过程中的噪声水平。我们还看到,行和列的转置对之间的相关性可以增强或抑制反馈效应,这取决于相关系数的符号。在gLVEs的背景下,行内和转置行/列相关性因此影响物种存活率和生态平衡的稳定性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generalized correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model.

In the study of disordered systems, one often chooses a matrix of independent identically distributed interaction coefficients to represent the quenched random couplings between components, perhaps with some symmetry constraint or correlations between diagonally opposite pairs of elements. However, a more general set of couplings, which still preserves the statistical interchangeability of the components, could involve correlations between interaction coefficients sharing only a single row or column index. These correlations have been shown to arise naturally in systems such as the generalized Lotka-Volterra equations (gLVEs). In this work, we perform a dynamic mean-field analysis to understand how single-index correlations affect the dynamics and stability of disordered systems, taking the gLVEs as our example. We show that in-row correlations raise the level of noise in the mean-field process, even when the overall variance of the interaction coefficients is held constant. We also see that correlations between transpose pairs of rows and columns can either enhance or suppress feedback effects, depending on the sign of the correlation coefficient. In the context of the gLVEs, in-row and transpose row/column correlations thus affect both the species survival rate and the stability of ecological equilibria.

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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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