Complexity, information transfer and collective behavior in
chaotic dynamical networks
Autores: M. Escalona-Morán, G. Paredes, M.G. Cosenza
Referencia: International Journal of Applied Mathematics and Statistics, 26, 58, (2011)
Abstract
We investigate the relationship between complexity,
information transfer and the emergence of collective
behaviors, such as synchronization and nontrivial
collective behavior, in a network of globally coupled
chaotic maps as a simple model of a complex system.
We calculate various quantities for this system: the
mean field, a measure of statistical complexity, the
information transfer, as well as the information
shared, between the macroscopic and local levels as
functions of the strength of a coupling parameter in
the system. Our results show that the emergence of
nontrivial collective behavior is associated to higher
values of complexity. Little transference of information
from the global to the local level occurs when the
system settles into nontrivial collective behavior while
no information at all flows between these two scales in
a synchronized collective state. As the parameter values
for the onset of nontrivial collective behavior or chaos
synchronization are approached, the information transfer
from the macroscopic level to the local level is higher,
in comparison to the situation where those collective
states are already established in the system. Our results
add support to the view of complexity as an emergent
collective property that is absent at the local level in
systems of interacting elements
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