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Effect of a distributed delay on relative stability of diffusely coupled systems, with application to synchronized equilibria
Author(s) -
Morărescu IrinelConstantin,
Michiels Wim,
Jungers Marc
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3368
Subject(s) - stability (learning theory) , coupling (piping) , stability theory , topology (electrical circuits) , control theory (sociology) , synchronization (alternating current) , class (philosophy) , computer science , exponential stability , function (biology) , mathematics , nonlinear system , physics , control (management) , engineering , mechanical engineering , quantum mechanics , machine learning , combinatorics , artificial intelligence , biology , evolutionary biology
Summary We perform a linear stability analysis of synchronized equilibria in networks of diffusely coupled oscillators, affected by distributed delays in the coupling, and we characterize the structure of the emanating solutions in the bifurcations, under the assumption that the delay kernels are equal to each other. The motivation comes from the fact that valuable quantitative and qualitative information about the occurrence and type of synchronous or partially synchronous solutions can be obtained from this linear analysis. We analyze stability of synchronized equilibria as a function of the parameters of a so‐called shifted gamma‐distributed delay, which allows to represent or approximate a large class of distributed delay kernels. We also present an asymptotic analysis method, which is particularly suitable for studying the effect of a distribution of delays on stability. We apply the methods to networks of coupled Lorenz systems, where we highlight that stability is favored by a distributed delay compared with a discrete delay with the same average value. Among others, we show that if the coupling is diffusive, the synchronized equilibria become asymptotically stable for large values of the coupling gain, that is, the systems locally asymptotically synchronize at an equilibrium, independently of the network topology. Copyright © 2015 John Wiley & Sons, Ltd.