19 research outputs found
Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps
The phenomena of synchronization and nontrivial collective behavior are
studied in a model of coupled chaotic maps with random global coupling. The
mean field of the system is coupled to a fraction of elements randomly chosen
at any given time. It is shown that the reinjection of the mean field to a
fraction of randomly selected elements can induce synchronization and
nontrivial collective behavior in the system. The regions where these
collective states emerge on the space of parameters of the system are
calculated.Comment: 2 pages, 2 figs, accepted in The European Physical Journa
Generalized synchronization of chaos in autonomous systems
We extend the concept of generalized synchronization of chaos, a phenomenon
that occurs in driven dynamical systems, to the context of autonomous
spatiotemporal systems. It means a situation where the chaotic state variables
in an autonomous system can be synchronized to each other but not to a coupling
function defined from them. The form of the coupling function is not crucial;
it may not depend on all the state variables nor it needs to be active for all
times for achieving generalized synchronization. The procedure is based on the
analogy between a response map subject to an external drive acting with a
probability p and an autonomous system of coupled maps where a global
interaction between the maps takes place with this same probability. It is
shown that, under some circumstances, the conditions for stability of
generalized synchronized states are equivalent in both types of systems. Our
results reveal the existence of similar minimal conditions for the emergence of
generalized synchronization of chaos in driven and in autonomous spatiotemporal
systems.Comment: 5 pages, 7 figures, accepted in PR
Phase separation in coupled chaotic maps on fractal networks
The phase ordering dynamics of coupled chaotic maps on fractal networks are
investigated. The statistical properties of the systems are characterized by
means of the persistence probability of equivalent spin variables that define
the phases. The persistence saturates and phase domains freeze for all values
of the coupling parameter as a consequence of the fractal structure of the
networks, in contrast to the phase transition behavior previously observed in
regular Euclidean lattices. Several discontinuities and other features found in
the saturation persistence curve as a function of the coupling are explained in
terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE
Chaos synchronization with coexisting global fields
We investigate the phenomenon of chaos synchronization in systems subject to coexisting autonomous and external global fields by employing a simple model of coupled maps. Two states of chaos synchronization are found: (i) complete synchronization, where the maps synchronize among themselves and to the external field, and (ii) generalized or internal synchronization, where the maps synchronize among themselves but not to the external global field. We show that the stability conditions for both states can be achieved for a system of minimum size of two maps. We consider local maps possessing robust chaos and characterize the synchronization states on the space of parameters of the system. The state of generalized synchronization of chaos arises even when the drive and the local maps have the same functional form. This behavior is similar to the process of spontaneous ordering against an external field found in nonequilibrium systems