Generalized correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model

• DOI: 10.1103/PhysRevE.111.044202
• ArXiv number: 2409.12751

In the study of disordered systems, one often chooses a matrix of independent identically distributed in- teraction 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.

• Artículo completo

Related research projects

MdM-IFISC-2

Maria de Maeztu 2023-2026

I.P.: Ernesto Estrada, Ingo Fischer, Emilio Hernández-García, Rosa Lopez, Claudio Mirasso, Jose Javier Ramasco, Raúl Toral, Roberta Zambrini

After 15 years of its existence, IFISC can point to a proven track record of impactful research. The previous 2018-2022 MdM award has significantly enhanced the institute's capabilities, as demonstrated by an …

APASOS

A Physics approach to sociotechnical systems: from theory to data analysis.

I.P.: Tobias Galla, Maxi San Miguel, Raúl Toral

APASOS objective is to use mathematical and computational methods combined with data and physics thinking to model complex socio-technical systems. APASOS is organized into two workpackages (WP). WP 1 focuses on models …