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Pinning generalized synchronization of dynamical networks via coordinate transformations

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  • Barajas-Ramírez, Juan Gonzalo
  • Ruiz-Silva, Adriana
  • Anzo-Hernández, Andrés

Abstract

A dynamical network achieves generalized synchronization if there exists an asymptotically stable manifold in which the solution of each node is uniquely determined as a static function of the states of any other node in the network. For bidirectionally coupled networks, the description of a synchronization manifold changes from pairwise-explicit form to an implicit form of the relationship between its nodes. Using this description, we start with a network of identical nodes that can be controlled towards a synchronization manifold, for this bidirectionally coupled network we propose a pinning strategy to impose a desired relation between nodes based on invertible coordinate transformations. We illustrate our results with numerical simulations of well-known chaotic benchmark systems.

Suggested Citation

  • Barajas-Ramírez, Juan Gonzalo & Ruiz-Silva, Adriana & Anzo-Hernández, Andrés, 2021. "Pinning generalized synchronization of dynamical networks via coordinate transformations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1164-1175.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1164-1175
    DOI: 10.1016/j.matcom.2021.07.008
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    References listed on IDEAS

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