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CATEGORIES:DAMTP Statistical Physics and Soft Matter Seminar
SUMMARY:Evidence of glassy phases in large interacting eco
systems with demographic noise - Ada Altieri (Labo
ratoire Matière et Systèmes Complexes\, Paris)
DTSTART;TZID=Europe/London:20201201T130000
DTEND;TZID=Europe/London:20201201T140000
UID:TALK153571AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/153571
DESCRIPTION:Zoom link: https://maths-cam-ac-uk.zoom.us/j/94018
037756\n\nMany complex systems in Nature\, from me
tabolic networks to ecosystems\, appear to be pois
ed at the edge of stability\, hence displaying eno
rmous responses to external perturbations. This fe
ature\, also known in physics as marginal stabilit
y\, is often the consequence of the complexity of
the underlying interaction network\, which can ind
uce large-scale collective dynamics and therefore
critical behaviour. \n\nIn this seminar\, I will p
resent the problem of ecological complexity by foc
ussing on a reference model in theoretical ecology
\, the high-dimensional Lotka-Volterra model with
random symmetric interactions and finite demograph
ic noise [1]. By using techniques rooted in mean-f
ield spin-glass theory\, I will show how to obtain
a complete characterisation of the phase diagrams
. Notably\, I will relate emerging collective beha
viours and slow relaxation dynamics to the emergen
ce of different disordered phases akin to those ta
king place in glassy systems [2\,3]. I will descr
ibe in particular: i) a multiple equilibria phase
\, which can be proven to be associated with an ex
ponential number of stable equilibria in the syste
m size\; ii) a marginally stable amorphous phase (
denoted as Gardner phase) as characterised by a hi
erarchical structure of these equilibria [1]. Fina
lly\, I will discuss the extension of our results:
i) to the case of weakly asymmetric interactions\
; ii) by considering a higher-order potential in t
he dynamics of the species abundances [4]\, which
turns out to be beneficial to model cooperative ef
fects in ecological and biological communities. \n
\n\n[1] A. Altieri\, F. Roy\, C. Cammarota\, G. Bi
roli\, Properties of equilibria and glassy phases
of the random Lotka-Volterra model with demographi
c noise\, arXiv:2009.10565 (2020).\n\n[2] P. Char
bonneau\, J. Kurchan\, G. Parisi\, P. Urbani\, Fra
ctal free energy landscapes in structural glasses\
, Nature Communications 5\, 3725 (2014).\n\n[3] A.
Altieri\, Jamming and Glass Transitions: In Mean-
Field Theory and Beyond\, Springer Nature (2019).\
n\n[4] A. Altieri\, G. Biroli\, The effect of spec
ies cooperation in large interacting ecosystems\,
in preparation.
LOCATION:via zoom\, meeting ID 940-1803-7756
CONTACT:Camille Scalliet
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