TY - JOUR
T1 - Generalized Lotka-Volterra Equations with Random, Nonreciprocal Interactions
T2 - The Typical Number of Equilibria
AU - Ros, Valentina
AU - Roy, Felix
AU - Biroli, Giulio
AU - Bunin, Guy
AU - Turner, Ari M.
N1 - Publisher Copyright: © 2023 American Physical Society.
PY - 2023/6/23
Y1 - 2023/6/23
N2 - We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e., of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.
AB - We compute the typical number of equilibria of the generalized Lotka-Volterra equations describing species-rich ecosystems with random, nonreciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similarity between equilibria as a function of their diversity (i.e., of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.
UR - http://www.scopus.com/inward/record.url?scp=85164246050&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.130.257401
DO - 10.1103/PhysRevLett.130.257401
M3 - مقالة
C2 - 37418712
SN - 0031-9007
VL - 130
JO - Physical Review Letters
JF - Physical Review Letters
IS - 25
M1 - 257401
ER -
