2024/11/05 by Onofrio Mazzarisi, Matteo Smerlak · 1 voice
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Social Sciences · #Argument (complex analysis) #Artificial intelligence #Biology #Biome #Complex system #Computer science #Dynamical systems theory #Ecology #Ecosystem dynamics and resilience #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Focus (optics) #Generalization #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Random matrix #Stability (learning theory) #Statistical physics
paper · doi:10.1103/physreve.110.054403
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.