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		<doi>10.1016/j.physd.2017.01.005</doi>
		<issn>0167-2789</issn>
		<citationkey>GrzybowskiMacaYone:2017:LyThSu</citationkey>
		<title>The Lyapunov–Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators</title>
		<year>2017</year>
		<month>May</month>
		<typeofwork>journal article</typeofwork>
		<secondarytype>PRE PI</secondarytype>
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		<author>Grzybowski, Jose M. V.,</author>
		<author>Macau, Elbert Einstein Nehrer,</author>
		<author>Yoneyama, T.,</author>
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		<group></group>
		<group>LABAC-COCTE-INPE-MCTIC-GOV-BR</group>
		<affiliation>Universidade Federal da Fronteira Sul (UFFS)</affiliation>
		<affiliation>Instituto Nacional de Pesquisas Espaciais (INPE)</affiliation>
		<affiliation>Instituto Tecnológico de Aeronáutica (ITA)</affiliation>
		<electronicmailaddress>jose.grzybowski@uffs.edu.br</electronicmailaddress>
		<electronicmailaddress>elbert.macau@inpe.br</electronicmailaddress>
		<journal>Physica D: Nonlinear Phenomena</journal>
		<volume>346</volume>
		<pages>28-36</pages>
		<secondarymark>A1_ENGENHARIAS_III A2_MATEMÁTICA_/_PROBABILIDADE_E_ESTATÍSTICA A2_INTERDISCIPLINAR A2_GEOCIÊNCIAS B1_MEDICINA_II B1_ENGENHARIAS_IV B1_ENGENHARIAS_II B2_ENSINO B2_CIÊNCIA_DA_COMPUTAÇÃO B2_ASTRONOMIA_/_FÍSICA</secondarymark>
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		<keywords>Chaotic systems, Isochronal synchronization, Lyapunov–Krasovskii.</keywords>
		<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, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the HindmarshRose neuron.</abstract>
		<area>COMP</area>
		<language>en</language>
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