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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.
It is shown that the synchronization behavior of a system of chaotic maps subject to either an external forcing or a coupling function of their internal variables can be inferred from the behavior of a single element in the system, which can be seen
The properties of functional relation between a non-invertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states
This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state error variable
In this article we synchronize by active control method all 19 identical Sprott systems provided in paper [10]. Particularly, we find the corresponding active controllers as well as we perform (as an example) the numerical synchronization of two Sprott-A models.
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize completely,