Geodesic
Generalized synchronization in the networks with directed acyclic structure
Kybernetika, Tome 59 (2023) no. 3, pp. 437-460
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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.
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.
DOI : 10.14736/kyb-2023-3-0437
Classification : 05C82, 34D06, 93C10
Keywords: generalized Lorenz system; generalized synchronization; chaos; networks 
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Čelikovský, Sergej; Lynnyk, Volodymyr; Lynnyk, Anna; Rehák, Branislav. Generalized synchronization in the networks with directed acyclic structure. Kybernetika, Tome 59 (2023) no. 3, pp. 437-460. doi: 10.14736/kyb-2023-3-0437

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