arXiv subjects

Juan Giral Martínez

Publications and source records attributed to Juan Giral Martínez.

3 recordsLinked to original sources

arXiv2025

A symmetry-based approach to species-rich ecological communities

Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality ensures that many microscopic details are irrelevant to system-wide dynamics; but the choice of a random ensemble still limits the generality of results. We show here, in the context of ecological dynamics, that these analytical tools do not require a specific choice of ensemble, and that solutions can be found based only on a fundamental rotational symmetry in the interactions, encoding the idea that traits can be recombined into new species without altering global features. Dynamical outcomes then depend on the spectrum of the interaction matrix as a free parameter, allowing us to bridge between results found in different models of interactions, and extend beyond them to previously unidentified behaviors. The distinctive feature of ecological models is the possibility of species extinctions, which leads to an increased universality of dynamics as the fraction of extinct species increases. We expect that these findings can inform new developments in theoretical ecology as well as for other families of complex systems.

q-bio.PE↗

arXiv2025

Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems

A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of organisms, or of individual species and their relations. Low-dimensional heuristic 'macroscopic' models that are widely used to capture ecological relationships -- and commonly evidence out-of equilibrium regimes -- implicitly assume that species-level 'microscopic' heterogeneity can be neglected. Here, we address the stability of such macroscopic descriptions to the addition of disordered microscopic interactions. We find that increased heterogeneity can stabilize collective as well as species fluctuations -- contrary to the well-known destabilizing effect of disorder on fixed points. We analytically find the conditions for the existence of heterogeneity-driven equilibria, and relate their stability to a mismatch in microscopic time scales. This may shed light onto the empirical observation that many-species ecosystems often appear stable at aggregated levels despite highly diverse interactions and large fluctuations at the species level.

q-bio.PE↗

arXiv2020

Young stellar cluster dilution near supermassive black holes: the impact of Vector Resonant Relaxation on neighbour separation

We investigate the rate of orbital orientation dilution of young stellar clusters in the vicinity of supermassive black holes. Within the framework of vector resonant relaxation, we predict the time evolution of the two-point correlation function of the stellar orbital plane orientations as a function of their initial angular separation and diversity in orbital parameters (semi-major axis, eccentricity). As expected, the larger the spread in initial orientations and orbital parameters, the more efficient the dilution of a given set of co-eval stars, with a characteristic timescale set up by the coherence time of the background potential fluctuations. A Markovian prescription which matches numerical simulations allows us to efficiently probe the underlying kinematic properties of the unresolved nucleus when requesting consistency with a given dilution efficiency, imposed by the observed stellar disc within the one arcsecond of Sgr A*. As a proof of concept, we compute maps of constant dilution times as a function of the semi major axis cusp index and fraction of intermediate mass black holes in the old background stellar cluster. This computation suggests that vector resonant relaxation should prove useful in this context since it impacts orientations on timescales comparable to the stars' age.

astro-ph.GA↗