Generalized synchronization of chaos in
autonomous systems
Authors: M.G. Cosenza, O. Alvarez-Llamoza
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
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