Synchronization patterns with strong memory adaptive control in networks of coupled neurons with chimera states dynamics

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

Chaos, Solitons & Fractals, 2019, vol. 128, issue C, 167-175

Abstract: This work presents the Hindmarsh–Rose fractional model of three-state using the Atangana–Baleanu–Caputo fractional derivative with strong memory. The model allows simulating the chimera states in a neural network. To achieve the synchronization was developed a fractional adaptive controller which is based on the uncertainty of the coupling parameters. The synchronization was studied using different fractional-orders and for 15, 40, 65 and 90 neurons. We consider fractional derivatives with nonlocal and non-singular Mittag-Leffler law. The simulations results show that the neurons synchronization is reached using the proposed method. 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; Parkinson disease; Hindmarsh–Rose model; Adaptive control (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:128:y:2019:i:c:p:167-175

DOI: 10.1016/j.chaos.2019.07.057

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