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Neural & Bio-inspired Processing and Robot Control

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Front. Neurorobot. | doi: 10.3389/fnbot.2018.00006

Robust adaptive synchronization of ring configured uncertain chaotic FitzHugh-Nagumo neurons under direction-dependent coupling

  • 1Pakistan Institute of Engineering and Applied Sciences, Pakistan
  • 2Pusan National University, South Korea

This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh-Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided.

Keywords: FitzHugh-Nagumo neuron, neuronal networks, Ring configuration, Coupling strengths, Robust adaptive synchronization control

Received: 01 Aug 2017; Accepted: 02 Feb 2018.

Edited by:

Muhammad U. Khan, Air University, Pakistan

Reviewed by:

Rongyu Tang, Beijing Institute of Technology, China
Huaguang Gu, Tongji University, China  

Copyright: © 2018 Iqbal, Rehan and Hong. 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 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: Dr. Muhammad Rehan, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan, rehanqau@gmail.com