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@Article{GrzybowskiMacaYone:2017:LyThSu,
               author = "Grzybowski, Jose M. V. and Macau, Elbert Einstein Nehrer and 
                         Yoneyama, T.",
          affiliation = "{Universidade Federal da Fronteira Sul (UFFS)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)} and {Instituto 
                         Tecnol{\'o}gico de Aeron{\'a}utica (ITA)}",
                title = "The Lyapunov–Krasovskii theorem and a sufficient criterion for 
                         local stability of isochronal synchronization in networks of 
                         delay-coupled oscillators",
              journal = "Physica D: Nonlinear Phenomena",
                 year = "2017",
               volume = "346",
                pages = "28--36",
                month = "May",
             keywords = "Chaotic systems, Isochronal synchronization, 
                         Lyapunov–Krasovskii.",
             abstract = "This paper presents a self-contained framework for the stability 
                         assessment of isochronal synchronization in networks of chaotic 
                         and limit-cycle oscillators. The results were based on the 
                         LyapunovKrasovskii theorem and they establish a sufficient 
                         condition for local synchronization stability of as a function of 
                         the system and network parameters. With this in mind, a network of 
                         mutually delay-coupled oscillators subject to direct self-coupling 
                         is considered and then the resulting error equations are 
                         block-diagonalized for the purpose of studying their stability. 
                         These error equations are evaluated by means of analytical 
                         stability results derived from the LyapunovKrasovskii theorem. The 
                         proposed approach is shown to be a feasible option for the 
                         investigation of local stability of isochronal synchronization for 
                         a variety of oscillators coupled through linear functions of the 
                         state variables under a given undirected graph structure. This 
                         ultimately permits the systematic identification of stability 
                         regions within the high-dimensionality of the network parameter 
                         space. Examples of applications of the results to a number of 
                         networks of delay-coupled chaotic and limit-cycle oscillators are 
                         provided, such as Lorenz, R{\"o}ssler, Cubic Chua's circuit, Van 
                         der Pol oscillator and the HindmarshRose neuron.",
                  doi = "10.1016/j.physd.2017.01.005",
                  url = "http://dx.doi.org/10.1016/j.physd.2017.01.005",
                 issn = "0167-2789",
             language = "en",
           targetfile = "grzy_lyapu.pdf",
        urlaccessdate = "27 nov. 2020"
}


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