title: Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.
abstract: This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.
authors.affiliation: Department of Electrical and Computer Engineering, Centre for Advanced Studies in Engineering (CASE), Islamabad 44000, Pakistan.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Iqbal
authors.affiliation: Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad 44000, Pakistan.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Rehan
authors.affiliation: Department of Electrical and Computer Engineering, Centre for Advanced Studies in Engineering (CASE), Islamabad 44000, Pakistan.
authors.forename: Abdul
authors.initials: A
authors.lastname: Khaliq
authors.affiliation: Department of Electrical and Computer Engineering, Centre for Advanced Studies in Engineering (CASE), Islamabad 44000, Pakistan.
authors.lastname: Saeed-ur-Rehman
authors.affiliation: Department of Cogno-Mechatronics Engineering and School of Mechanical Engineering, Pusan National University, 2 Busandaehak-ro, Geumjeong-gu, Busan 609-735, Republic of Korea.
authors.forename: Keum-Shik
authors.initials: KS
authors.lastname: Hong
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D003198:Computer Simulation; D046690:Deep Brain Stimulation; D004558:Electric Stimulation; D006801:Humans; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000378:metabolism / Q000502:physiology; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results
references.citation: Neurotherapeutics. 2008 Apr;5(2):320-30
references.pmid: 18394573
references.citation: Comput Math Methods Med. 2012;2012:230980
references.pmid: 23197990
references.citation: Nat Rev Neurosci. 2005 Apr;6(4):285-96
references.pmid: 15803160
references.citation: Brain Res Brain Res Rev. 2004 Dec;47(1-3):191-215
references.pmid: 15572172
references.citation: J Theor Biol. 2011 Nov 21;289:151-9
references.pmid: 21893072
references.citation: Neurotherapeutics. 2008 Apr;5(2):309-19
references.pmid: 18394572
references.citation: Epilepsy Res. 2010 Mar;89(1):154-61
references.pmid: 19766458
references.citation: Comput Math Methods Med. 2013;2013:513187
references.pmid: 23533541
references.citation: Neuroscience. 2010 Jun 2;167(4):1032-43
references.pmid: 20211698
references.citation: Comput Math Methods Med. 2013;2013:182145
references.pmid: 24416069
references.citation: Comput Math Methods Med. 2013;2013:238937
references.pmid: 24194786
references.citation: Comput Math Methods Med. 2014;2014:174274
references.pmid: 24516505