Network synchronization of time-delayed coupled nonlinear systems using predictor-based diffusive dynamic couplings

Chaos
C MurguiaHenk Nijmeijer

Abstract

We study the problem of controlled network synchronization of coupled semipassive systems in the case when the outputs (the coupling variables) and the inputs are subject to constant time-delay (as it is often the case in a networked context). Predictor-based dynamic output feedback controllers are proposed to interconnect the systems on a given network. Using Lyapunov-Krasovskii functional and the notion of semipassivity, we prove that under some mild assumptions, the solutions of the interconnected systems are globally ultimately bounded. Sufficient conditions on the systems to be interconnected, on the network topology, on the coupling dynamics, and on the time-delays that guarantee global state synchronization are derived. A local analysis is provided in which we compare the performance of our predictor-based control scheme against the existing static diffusive couplings available in the literature. We show (locally) that the time-delay that can be induced to the network may be increased by including the predictors in the loop. The results are illustrated by computer simulations of coupled Hindmarsh-Rose neurons.

References

Mar 22, 1984·Proceedings of the Royal Society of London. Series B, Containing Papers of a Biological Character·J L Hindmarsh, R M Rose
Jun 1, 1994·Journal of Computational Neuroscience·C M Gray
Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H U Voss
Dec 3, 2008·Chaos·Toshiki OguchiTakashi Yamamoto
Jun 18, 2010·International Journal of Neural Systems·P J NeefsH Nijmeijer
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ikkyu AiharaKazuyuki Aihara
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Anton A SelivanovEckehard Schöll

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Citations

Dec 7, 2018·Chaos·Henning U Voss

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