TY - JOUR
T1 - Numerical implementation of dynamical mean field theory for disordered systems
T2 - Application to the Lotka-Volterra model of ecosystems
AU - Roy, F.
AU - Biroli, G.
AU - Bunin, G.
AU - Cammarota, C.
PY - 2019/11/5
Y1 - 2019/11/5
N2 - Dynamical mean field theory (DMFT) is a tool that allows one to analyze the stochastic dynamics of N interacting degrees of freedom in terms of a self-consistent 1-body problem. In this work, focusing on models of ecosystems, we present the derivation of DMFT through the dynamical cavity method, and we develop a method for solving it numerically. Our numerical procedure can be applied to a large variety of systems for which DMFT holds. We implement and test it for the generalized random Lotka-Volterra model, and show that complex dynamical regimes characterized by chaos and aging can be captured and studied by this framework.
AB - Dynamical mean field theory (DMFT) is a tool that allows one to analyze the stochastic dynamics of N interacting degrees of freedom in terms of a self-consistent 1-body problem. In this work, focusing on models of ecosystems, we present the derivation of DMFT through the dynamical cavity method, and we develop a method for solving it numerically. Our numerical procedure can be applied to a large variety of systems for which DMFT holds. We implement and test it for the generalized random Lotka-Volterra model, and show that complex dynamical regimes characterized by chaos and aging can be captured and studied by this framework.
KW - disordered systems
KW - non-equilibrium dynamics
KW - population dynamics
UR - http://www.scopus.com/inward/record.url?scp=85072324916&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ab1f32
DO - 10.1088/1751-8121/ab1f32
M3 - Article
AN - SCOPUS:85072324916
SN - 1751-8113
VL - 52
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 48
M1 - 484001
ER -