East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SYNCHRONIZATION OF UNIDIRECTIONAL RING STRUCTURED IDENTICAL FITZHUGH-NAGUMO NETWORK UNDER IONIC AND EXTERNAL ELECTRICAL STIMULATIONS

  • Received : 2020.01.02
  • Accepted : 2020.07.27
  • Published : 2020.09.30
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Abstract

Synchronization of unidirectional identical FitzHugh-Nagumo systems coupled in a ring structure under ionic and external electrical stimulations is investigated. In this network, each neuron is only connected and transmit signals to its next neuron via synaptic strength called gapjunctions. Adaptive control theory and Lyapunov stability theory are used to propose a unique control scheme with necessary and sufficient conditions which guarantee the synchronization of the neuronal network. Finally, the effectiveness of the proposed scheme is shown through numerical simulations.

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References

  1. Ibrahim, Malik Muhammad and Jung, Il Hyo, Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons With Single-and Dual-State Gap Junctions Under Ionic Gates and External Electrical Disturbance, IEEE Access(2019),vol. 7, 57894-57906. https://doi.org/10.1109/ACCESS.2019.2913872
  2. Che, Yan-Qiu and Wang, Jiang and Cui, Shi-Gang and Deng, Bin and Wei, Xi-Le and Chan, Wai-Lok and Tsang, Kai-Ming, Chaos synchronization of coupled neurons via adaptive sliding mode control, Nonlinear Analysis: Real World Application(2011),vol.12, no. 6, 3199-3206. https://doi.org/10.1016/j.nonrwa.2011.05.020
  3. Pecora, Louis M and Carroll, Thomas L, Synchronization in chaotic systems, Physical review letters(1990), vol. 64, no. 8, 821, 1990. https://doi.org/10.1103/PhysRevLett.64.821
  4. Yu, Haitao and Wang, Jiang and Deng, Bin and Wei, Xile and Che, Yanqiu and Wong, YK and Chan, WL and Tsang, KM, Adaptive backstepping sliding mode control for chaos synchronization of two coupled neurons in the external electrical stimulation, Communications in Nonlinear Science and Numerical Simulation (2012),Vol. 17, no. 3, 1344-1354. https://doi.org/10.1016/j.cnsns.2011.07.009
  5. Freund, Hans-Joachim, Motor unit and muscle activity in voluntary motor control, Physiological Reviews(1983),vol. 63, no. 2, 387-436. https://doi.org/10.1152/physrev.1983.63.2.387
  6. Levy, Ron and Hutchison, William D and Lozano, Andres M and Dostrovsky, Jonathan O, High-frequency synchronization of neuronal activity in the subthalamic nucleus of parkinsonian patients with limb tremor, Journal of Neuroscience (2000), Vol. 20, no. 20, 7766-7775 https://doi.org/10.1523/JNEUROSCI.20-20-07766.2000
  7. Sun, Xiaojuan and Li, Guofang, Synchronization transitions induced by partial time delay in a excitatory{inhibitory coupled neuronal network, Nonlinear Dynamics(2017), vol. 89, no. 4, 2509-2520. https://doi.org/10.1007/s11071-017-3600-4
  8. Wang, Jiang and Deng, Bin and Fei, Xiangyang, Chaotic synchronization of two coupled neurons via nonlinear control in external electrical stimulation, Chaos, Solitons & Fractals (2006), vol. 27, no. 5, 1272-1278. https://doi.org/10.1016/j.chaos.2005.04.102
  9. Mishra, Deepak and Yadav, Abhishek and Ray, Sudipta and Kalra, Prem K, Controlling synchronization of modified Fitzhugh-Nagumo neurons under external electrical stimulation, IFAC-PapersOnLine (2006), vol. 4, no. 1.
  10. Che, Yan-Qiu and Wang, Jiang and Chan, Wai-Lok and Tsang, Kai-Ming, Chaos synchronization of coupled neurons under electrical stimulation via robust adaptive fuzzy control," Nonlinear Dynamics, , 2010., Nonlinear Dynamics(2010) vol. 61, no. 4, 847-857. https://doi.org/10.1007/s11071-010-9691-9
  11. Plotnikov, Sergei A, Control of synchronization in two delay-coupled FitzHugh-Nagumo systems with heterogeneities, IFAC-PapersOnLine (2015), vol. 48, no. 11, 887-891.
  12. Tehrani, Niloofar Farajzadeh and Razvan, MohammadReza, Bifurcation structure of two coupled FHN neurons with delay, Mathematical biosciences(2015), vol. 270, 41-56. https://doi.org/10.1016/j.mbs.2015.09.008
  13. Armanyos, Mina and Radwan, Ahmed G and Madian, Ahmed H, Fractional-order synchronization of two neurons using Fitzhugh-Nagumo neuron model, 2016 3rd International Conference on Advances in Computational Tools for Engineering Applications (ACTEA) (2016),168-171.
  14. Plotnikov, Sergei A and Fradkov, Alexander L, Controlled synchronization in two hybrid FitzHugh-Nagumo systems, IFAC-PapersOnLine (2016), vol. 49, no. 14, 137-141.
  15. Saha, Arindam and Feudel, Ulrike, Extreme events in FitzHugh-Nagumo oscillators coupled with two time delays, Physical Review E (2017), vol. 95, no. 6, 062219. https://doi.org/10.1103/PhysRevE.95.062219
  16. Zhen, Bin and Li, Zhenhua and Song, Zigen, Influence of Time Delay in Signal Transmission on Synchronization between Two Coupled FitzHugh-Nagumo Neurons, Applied Sciences (2019), vol. 9, no. 10, 2159. https://doi.org/10.3390/app9102159
  17. Kamran, Muhammad A and Mannan, Malik M Naeem and Jeong, Myung Yung, Cortical signal analysis and advances in functional near-infrared spectroscopy signal: a review, Frontiers in human neuroscience(2016), vol. 10, 261. https://doi.org/10.3389/fnhum.2016.00261
  18. Mannan, Malik M Naeem and Kim, Shinjung and Jeong, Myung Yung and Kamran, M Ahmad, Hybrid EEGEye tracker: Automatic identification and removal of eye movement and blink artifacts from electroencephalographic signal, Sensors (2016), vol. 16, no. 2, 241. https://doi.org/10.3390/s16020241
  19. Mannan, Malik M Naeem and Jeong, Myung Y and Kamran, Muhammad A, Hybrid ICARegression: automatic identification and removal of ocular artifacts from electroen-cephalographic signals, Frontiers in human neuroscience (2016), vol. 10, 193. https://doi.org/10.3389/fnhum.2016.00193
  20. Mannan, Malik M Naeem and Kamran, M Ahmad and Kang, Shinil and Jeong, Myung Yung, Effect of EOG signal filtering on the removal of ocular artifacts and EEG-based brain-computer interface: A comprehensive study, Complexity (2018, vol. 2018.