Relating high dimensional stochastic complex systems to low-dimensional intermittency
File(s)
Accepted version
Author(s)
Diaz-Ruelas, A
Jensen, HJ
Piovani, D
Robledo, A
Type
Journal Article
Abstract
We evaluate the implication and outlook of an unanticipated
simplification in the macroscopic behavior of two high-dimensional stochastic
models: the Replicator Model with Mutations and the Tangled
Nature Model (TaNa) of evolutionary ecology. This simplification consists
of the apparent display of low-dimensional dynamics in the nonstationary
intermittent time evolution of the model on a coarse-grained
scale. Evolution on this time scale spans generations of individuals,
rather than single reproduction, death or mutation events. While a local
one-dimensional map close to a tangent bifurcation can be derived
from a mean-field version of the TaNa model, a nonlinear dynamical
model consisting of successive tangent bifurcations generates time evolution
patterns resembling those of the full TaNa model. To advance
the interpretation of this finding, here we consider parallel results on a
game-theoretic version of the TaNa model that in discrete time yields
a coupled map lattice. This in turn is represented, a la Langevin, by
a one-dimensional nonlinear map. Among various kinds of behaviours
we obtain intermittent evolution associated with tangent bifurcations.
We discuss our results.
simplification in the macroscopic behavior of two high-dimensional stochastic
models: the Replicator Model with Mutations and the Tangled
Nature Model (TaNa) of evolutionary ecology. This simplification consists
of the apparent display of low-dimensional dynamics in the nonstationary
intermittent time evolution of the model on a coarse-grained
scale. Evolution on this time scale spans generations of individuals,
rather than single reproduction, death or mutation events. While a local
one-dimensional map close to a tangent bifurcation can be derived
from a mean-field version of the TaNa model, a nonlinear dynamical
model consisting of successive tangent bifurcations generates time evolution
patterns resembling those of the full TaNa model. To advance
the interpretation of this finding, here we consider parallel results on a
game-theoretic version of the TaNa model that in discrete time yields
a coupled map lattice. This in turn is represented, a la Langevin, by
a one-dimensional nonlinear map. Among various kinds of behaviours
we obtain intermittent evolution associated with tangent bifurcations.
We discuss our results.
Date Issued
2017-03-06
Date Acceptance
2016-10-19
Citation
European Physical Journal - Special Topics, 2017, 226 (3), pp.341-351
ISSN
1951-6355
Publisher
Springer
Start Page
341
End Page
351
Journal / Book Title
European Physical Journal - Special Topics
Volume
226
Issue
3
Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60264-4
Subjects
Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics
TANGLED NATURE
MODEL
EMERGENCE
DYNAMICS
Publication Status
Published