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

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. (C) 2019 Elsevier Ltd. All rights reserved.