M. S. Palmero | Searcharxiv

arXiv2025

Investigating Mobility in Spatial Biodiversity Models through Recurrence Quantification Analysis

Recurrence plots and their associated quantifiers provide a robust framework for detecting and characterising complex patterns in non-linear time-series. In this paper, we employ recurrence quantification analysis to investigate the dynamics of the cyclic, non-hierarchical May-Leonard model, also referred to as rock--paper--scissors systems, that describes competitive interactions among three species. A crucial control parameter in these systems is the species' mobility $m$, which governs the spatial displacement of individuals and profoundly influences the resulting dynamics. By systematically varying $m$ and constructing suitable recurrence plots from numerical simulations, we explore how recurrence quantifiers reflect distinct dynamical features associated with different ecological states. We then introduce an ensemble-based approach that leverages statistical distributions of recurrence quantifiers, computed from numerous independent realisations, allowing us to identify dynamical outliers as significant deviations from typical system behaviour. Through detailed numerical analyses, we demonstrate that these outliers correspond to divergent ecological regimes associated with specific mobility values, providing also a robust manner to infer the mobility parameter from observed numerical data. Our results highlight the potential of recurrence-based methods as diagnostic tools for analysing spatial ecological systems and extracting ecologically relevant information from their non-linear dynamical patterns.

q-bio.PE↗

arXiv2025

Parameter Inference in Non-linear Dynamical Systems via Recurrence Plots and Convolutional Neural Networks

Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on system-specific models and involve heavily parametrised formulations, which can limit their general applicability. In this study, we present a methodology that employs recurrence plots as structured representations of non-linear trajectories, which are then used to train convolutional neural networks to infer the values of the control parameter associated with the analysed trajectories. We focus on two representative non-linear systems, namely the logistic map and the standard map, and show that our approach enables accurate estimation of the parameters governing their dynamics. When compared to regression models trained directly on raw time-series data, the use of recurrence plots yields significantly more robust results. Although the methodology does not aim to predict future states explicitly, we argue that accurate parameter inference, when combined with predetermined initial conditions, enables the reconstruction of a system's evolution due to its deterministic nature. These findings highlight the potential of recurrence-based learning frameworks for the automated identification and characterisation of non-linear dynamical behaviours.

nlin.CD↗