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On the Controlled Synchronization of Dynamical Networks with Non Identical Nodes

Juan Gonzalo Barajas Ramirez, Ricardo Femat
On this contribution, the problem of chaos synchronization on networks of structurally
different dynamical systems is investigated. Synchronization of dynamical networks is usually define
in terms of identical accordance on the evolution of each individual node in the network. However,
for a network consisting of strictly different nodes, this type of synchronization may not be possible.
However, a generalized definition of synchronization can be introduced where the evolution of each
node can be related to the others in terms of a given transformation. In particular, in this study the
case considered is that of systems of identical dimension that can be express in a canonical form by
an appropriately chosen coordinate transformation. In order to determine conditions under which
a network of strictly different nodes can achieve a generalized synchronization, a local robust controller
is designed to forces the network to synchronize in terms of its transformed coordinates. The
main results of this study are illustrated by numerical simulations of a network of well-known chaotic
benchmark systems.
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