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Front. Neurosci. | doi: 10.3389/fnins.2019.01061

Unidirectional Synchronization of Hodgkin-Huxley Neurons with Prescribed Performance under Transcranial Magneto-Acoustical Simulation

 Dan Liu1, Song Zhao2, Xiaoyuan Luo1 and  Yi Yuan1*
  • 1Yanshan University, China
  • 2Hebei Medical University, China

This paper exploits the unidirectional synchronization dynamics of two Hodgkin-Huxley(HH) neurons under transcranial magneto-acoustical stimulation (TMAS). The major purpose is to explore a control scheme to make the spiking modes of the neural potentials stimulated by TMAS achieve synchronization states under the feedback input. For this purpose, an adaptive neural controller, which makes the neurons satisfy the prescribed master-slaver synchronization performance, is designed by introducing a tracking error into Lyapunov analysis. Under the proposed control scheme, the slaver neuron can not only overcome the model uncertainties and the difficulties brought by prescribed performance, but also track the spiking patterns of the master neuron. Finally, the simulations are implemented to demonstrate the effectiveness of the proposed controller, that is, the TMAS induced synchronization states of the HH neuron system can achieve the prescribed performance under the proposed controller.

Keywords: TMAS, Hodgkin-Huxley Neuron, unidirectional synchronization, Adaptive neural control, Predefined performance

Received: 04 Jan 2019; Accepted: 20 Sep 2019.

Copyright: © 2019 Liu, Zhao, Luo and Yuan. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Yi Yuan, Yanshan University, Qinhuangdao, China, yuanyi513@ysu.edu.cn