Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics

P. Vázquez-Guerrero, J.F. Gómez-Aguilar, F. Santamaria and R.F. Escobar-Jiménez

Physica A: Statistical Mechanics and its Applications, 2020, vol. 539, issue C

Abstract: In this paper, we propose a high-gain observer to synchronize chimera states in coupled neurons with fractional dynamics. The observer allows the synchronization with a master–slave topology. The master describes a dynamical system in state-space representation, whereas the slave is described by a high-gain state observer. The fractional differential equations are described by the Riemann–Liouville fractional derivative, also for non-local conformable derivatives and Atangana–Baleanu operators both in Caputo sense. We present numerical simulations involving the synchronization of Hindmarsh–Rose and Hodgking–Huxley models. The numerical simulations showed that the chimera states can be synchronized using fractional derivatives. We believe that the application of fractional operators to synchronization of Chimera states open a new direction of research in the near future.

Keywords: Fractional calculus; Chimera states; Synchronization; Hindmarsh–Rose model; Hodgking–Huxley model (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:539:y:2020:i:c:s0378437119316449

DOI: 10.1016/j.physa.2019.122896

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