Equivalent synchronization of chaos in driven and
in autonomous systems
Autores: M.G. Cosenza, O. Alvarez-Llamoza, G. Paredes
Referencia:
Journal of Physics: Conference Series, 246, 012009, (2010)
Abstract
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 as a single drive-response
map. From the conditions for stable
synchronization in this single driven-map model
with minimal ingredients, we find minimal
conditions for the emergence of complete and
generalized chaos synchronization in both
driven and autonomous associated systems. Our
results show that the presence of a common
drive or a coupling function for all times is
not indispensable for reaching synchronization
in a system of chaotic oscillators, nor is the
simultaneous sharing of a field, either external
or endogenous, by all the elements. In the case
of an autonomous system, the coupling function
does not need to depend on all the internal
variables for achieving synchronization and its
functional form is not crucial for generalized
synchronization. What becomes essential for
reaching synchronization in an extended system is
the sharing of some minimal information by its
elements, on the average, over long times,
independently of the nature (external or
internal) of its source
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