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Significance Understanding how communities emerge from a large number of interacting entities is a long-standing question in several fields. In ecosystems with randomly coupled species, a delayed dynamics seemed to… Click to show full abstract
Significance Understanding how communities emerge from a large number of interacting entities is a long-standing question in several fields. In ecosystems with randomly coupled species, a delayed dynamics seemed to play a minor role in characterizing the stability close to equilibrium. Here, we study the effects on large ecosystems of species’ interactions that are random as well as delayed. We find that near equilibrium, delayed self-interactions greatly modify the eigenspectrum distribution as predicted by Wigner’s as well as Girko’s laws. We analytically calculate the ensued generalized laws and identify the geometric profile of the eigenvalues in the complex plane.
Journal Title: Proceedings of the National Academy of Sciences of the United States of America
Year Published: 2022
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