ABSTRACT
We investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external (driven systems) or internal (autonomous systems). By employing general models of coupled chaotic maps for such systems, we show that the presence of a homogeneous global field, either external or internal, for all times is not indispensable for achieving complete or generalized synchronization in a system of chaotic elements. Complete synchronization can also appear with heterogeneous global fields; it does not requires the simultaneous sharing of the field by all the elements in a system. We use the normalized mutual information and the information transfer between global and local variables to characterize complete and generalized synchronization. We show that these information measures can characterize both types of synchronized states and also allow us to discern the origin of a global interaction field. A synchronization state emerges when a sufficient amount of information provided by a field is shared by all the elements in the system, on the average over long times. Thus, the maximum value of the top-down information transfer can be used as a predictor of synchronization in a system, as a parameter is varied.
ABSTRACT
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 does it need to be active for all times for achieving generalized synchronization. The procedure is based on an 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.
ABSTRACT
The phase ordering dynamics of coupled chaotic maps on fractal networks is 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.
