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

TL;DR

This paper introduces a nonlinear saturation into generalized Lotka-Volterra models with random interactions, improving ecological realism by preventing unbounded growth and revealing complex dynamical regimes.

Contribution

It develops an analytical framework for nonlinear GLV systems with quenched randomness, extending stability analysis and uncovering new dynamical behaviors.

Findings

Saturating nonlinearity suppresses unbounded growth.

Analytical species abundance distribution derived.

Transition between chaotic and low-volatility regimes observed.

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.