On the Controlled Synchronization of DynamicalNetworks with Non Identical Nodes

TL;DRAbstract

The problem of chaos synchronization on networks of structurally different dynamical systems is investigated. Synchronization of dynamical networks is usually defined 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 should be redefined. In this case, a generalized definition of synchronization can be considered, where the evolution of each node can be related to others in terms of a map. In this study, the case of systems that can be expressed in canonical form by an appropriately chosen coordinate transformation. In order to achieve generalized synchronization on a network of strictly different nodes, local robust controllers are designed which force the network to synchronize in terms of their 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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