Dresden 2026 – scientific programme
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BP: Fachverband Biologische Physik
BP 17: Statistical Physics of Biological Systems I (joint session DY/BP)
BP 17.12: Talk
Wednesday, March 11, 2026, 12:30–12:45, ZEU/0114
Local equations for the generalized Lotka-Volterra model on sparse asymmetric graphs — •David Machado Pérez1,2,3, Pietro Valigi1, Tommaso Tonolo4,5, and Maria Chiara Angelini6 — 1Physics Department, Sapienza University of Rome, Rome I-00185, Italy — 2Department of Theoretical Physics, Physics Faculty, University of Havana. CP10400, Havana, Cuba — 3CNR-NANOTEC, Rome Unit, Rome I-00185, Italy — 4Gran Sasso Science Institute, 67100 L'Aquila, Italy — 5INFN-Laboratori Nazionali del Gran Sasso, 67100 Assergi (AQ), Italy — 6INFN, Sezione di Roma I, 00185 Rome, Italy
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By deriving local Fokker-Planck equations and employing a mean-field closure, we can efficiently compute stationary states for both symmetric and asymmetric interactions. We validate our approach by comparing the results with the direct integration of the dynamical equations and by reproducing known results and, for the first time, we map the phase diagram for sparse asymmetric networks. Our framework provides a versatile tool for exploring stability in realistic ecological communities and can be generalized to applications in different contexts, such as economics and evolutionary game theory.
Keywords: generalized Lotka-Volterra model; sparse graphs; asymmetric interactions; Fokker-Planck equations; Local dynamical closures