@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 = "15 jun. 2024"
}