Dissimilarity measures for generalized Lotka-Volterra systems on networks

TL;DR

This paper introduces a comprehensive framework for measuring dissimilarities in generalized Lotka-Volterra systems on networks, capturing dynamics across various parameters and structures to analyze stability and robustness.

Contribution

The paper presents a novel, versatile dissimilarity measure framework applicable to diverse nonlinear dynamical systems on networks, including modifications with different equations.

Findings

Structural changes significantly affect system divergence.

Interaction strength and initial conditions influence dynamics.

Negative interactions impact stability transitions.

Abstract

In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The proposed measures capture both transient and stationary dynamics, allowing systematic comparisons across systems with varying interaction parameters, network weights, or topologies. Our analysis shows that even subtle structural changes can lead to markedly distinct outcomes: in two-species systems, interaction strength and initial conditions strongly affect divergence, while in small directed networks, differences that are invisible at the adjacency-matrix level produce divergent dynamics. In modular networks, the fraction and distribution of negative interactions control the transition from stable to unstable dynamics, with localized perturbations within cliques yielding different global outcomes than distributed ones. Beyond structural variations, the framework also applies when modified processes follow distinct nonlinear equations, demonstrating its versatility. Taken together, these results highlight that dynamical dissimilarity measures provide a powerful tool to analyze robustness, detect structural sensitivity, and predict instabilities in nonlinear systems. More broadly, this approach supports the comparative analysis of biological systems, where complex interaction networks and nonlinear dynamics are central to stability and resilience.