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Generalized Lotka-Volterra systems with quenched random interactions and saturating nonlinear response

Marco Zenari1,2,*, Francesco Ferraro1,3,4, Sandro Azaele1,3,4, Amos Maritan1,3,4, and Samir Suweis1,2,3

  • 1Department of Physics and Astronomy “Galileo Galilei”, University of Padova, Italy
  • 2Padova Neuroscience Center, University of Padova, Italy
  • 3INFN, Padova Division, Italy
  • 4National Biodiversity Future Center, Palermo, Italy

  • *Contact author: marco.zenari.2@phd.unipd.it
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Phys. Rev. E 113, 024206 – Published 12 February, 2026

DOI: https://doi.org/10.1103/hyxm-vxgy

Abstract

The generalized Lotka-Volterra (GLV) equations with quenched random interactions have been extensively used to investigate the stability and dynamics of complex ecosystems. However, the standard linear interaction model suffers from pathological unbounded growth, especially under strong cooperation or heterogeneity. This work addresses that limitation by introducing a Monod-type saturating nonlinear response into the GLV framework. Using Dynamical Mean-Field Theory, we derive analytical expressions for the species abundance distribution in the Unique Fixed Point phase and show the suppression of unbounded dynamics. Numerical simulations reveal a rich dynamical structure in the Multiple Attractor phase, including a transition between high-dimensional chaotic and low-volatility regimes, governed by interaction symmetry. These findings offer a more ecologically realistic foundation for disordered ecosystem models and highlight the role of nonlinearity and symmetry in shaping the diversity and resilience of large ecological communities.

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Information

Phys. Rev. E 113, 024206– Published 12 February, 2026
  • Received 5 June 2025
  • Accepted 13 January 2026
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