Generalized synchronization in the networks with directed acyclic structure

Sergej Čelikovský; Volodymyr Lynnyk; Anna Lynnyk; Branislav Rehák

Kybernetika (2023)

  • Volume: 59, Issue: 3, page 437-460
  • ISSN: 0023-5954

Abstract

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Generalized synchronization in the direct acyclic networks, i.e. the networks represented by the directed tree, is presented here. Network nodes consist of copies of the so-called generalized Lorenz system with possibly different parameters yet mutually structurally equivalent. The difference in parameters actually requires the generalized synchronization rather than the identical one. As the class of generalized Lorenz systems includes the well-known particular classes such as (classical) Lorenz system, Chen system, or Lü system, all these classes can be synchronized using the presented approach as well. The main theorem is rigorously mathematically formulated and proved in detail. Extensive numerical simulations are included to illustrate and further substantiate these theoretical results. Moreover, during these numerical experiments, the so-called duplicated system approach is used to double-check the generalized synchronization.

How to cite

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Čelikovský, Sergej, et al. "Generalized synchronization in the networks with directed acyclic structure." Kybernetika 59.3 (2023): 437-460. <http://eudml.org/doc/299449>.

@article{Čelikovský2023,
abstract = {Generalized synchronization in the direct acyclic networks, i.e. the networks represented by the directed tree, is presented here. Network nodes consist of copies of the so-called generalized Lorenz system with possibly different parameters yet mutually structurally equivalent. The difference in parameters actually requires the generalized synchronization rather than the identical one. As the class of generalized Lorenz systems includes the well-known particular classes such as (classical) Lorenz system, Chen system, or Lü system, all these classes can be synchronized using the presented approach as well. The main theorem is rigorously mathematically formulated and proved in detail. Extensive numerical simulations are included to illustrate and further substantiate these theoretical results. Moreover, during these numerical experiments, the so-called duplicated system approach is used to double-check the generalized synchronization.},
author = {Čelikovský, Sergej, Lynnyk, Volodymyr, Lynnyk, Anna, Rehák, Branislav},
journal = {Kybernetika},
keywords = {generalized Lorenz system; generalized synchronization; chaos; networks},
language = {eng},
number = {3},
pages = {437-460},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalized synchronization in the networks with directed acyclic structure},
url = {http://eudml.org/doc/299449},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Čelikovský, Sergej
AU - Lynnyk, Volodymyr
AU - Lynnyk, Anna
AU - Rehák, Branislav
TI - Generalized synchronization in the networks with directed acyclic structure
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 3
SP - 437
EP - 460
AB - Generalized synchronization in the direct acyclic networks, i.e. the networks represented by the directed tree, is presented here. Network nodes consist of copies of the so-called generalized Lorenz system with possibly different parameters yet mutually structurally equivalent. The difference in parameters actually requires the generalized synchronization rather than the identical one. As the class of generalized Lorenz systems includes the well-known particular classes such as (classical) Lorenz system, Chen system, or Lü system, all these classes can be synchronized using the presented approach as well. The main theorem is rigorously mathematically formulated and proved in detail. Extensive numerical simulations are included to illustrate and further substantiate these theoretical results. Moreover, during these numerical experiments, the so-called duplicated system approach is used to double-check the generalized synchronization.
LA - eng
KW - generalized Lorenz system; generalized synchronization; chaos; networks
UR - http://eudml.org/doc/299449
ER -

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