International Journal of Nonlinear Analysis and Applications

Synchronization between two coupled fractional order neuron models using the optimized fuzzy logic controller in the presence of external disturbances

Document Type : Research Paper

Authors

1 Department of Control Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Control Engineering, K.N. Toosi University of Technology, Tehran, Iran

Abstract

Appropriate modeling of the coupled neurons helps us understand neurons' natural functions. In this paper fuzzy logic controller has been designed to synchronize two coupled neuron models. The fractional-order neurons are based on the FitzHugh-Nagumo (FHN) model. An optimized fuzzy controller is designed to synchronize the behavior of two neurons with each other in the presence of external disturbances. This controller overcomes the disturbance. The simulation example shows the performance of the proposed method.

Keywords

[1] A. Akg¨ul, K. Rajagopal, A. Durdu, M.A. Pala, O.F. Boyraz and M.Z. Yildiz, ¨ A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application, Chaos Solitons Fractals 152 (2021), p. 111306.
[2] M. Aqil, K.-S. Hong and M.-Y. Jeong, Synchronization of coupled chaotic FitzHugh–Nagumo systems, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), no. 4, 1615–1627.
[3] R. Behinfaraz and M.A. Badamchizadeh, New approach to synchronization of two different fractional-order chaotic systems, Int. Symp. Artif. Intell. Signal Process. (AISP), IEEE, 2015.
[4] R. Behinfaraz and M.A. Badamchizadeh, Synchronization of different fractional order chaotic systems with timevarying parameter and orders, ISA Trans. 80 (2018), 399–410.
[5] R. Behinfaraz, S. Ghaemi and S. Khanmohammadi, Risk assessment in control of fractional-order coronary artery system in the presence of external disturbance with different proposed controllers, Appl. Soft Comput. 77 (2019), 290–299.
[6] J.C. Bezdek, Fuzziness vs. probability-again (!?), IEEE Trans. Fuzzy Syst. 2 (1994), no. 1, 1–3.
[7] S. Bhalekar and V. Daftardar-Gejji, Synchronization of different fractional order chaotic systems using active control, Commun. Nonlinear Sci. Numer. Simul. 15 (2010), no. 11, 3536–3546.
[8] S.Y. Chiu, J.M. Ritchie, R.B. Rogart and D. Stagg, A quantitative description of membrane currents in rabbit myelinated nerve, J. Phys. 292 (1979), no. 1, 149–166.
[9] R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, MHS’95. Proc. Sixth Int. Symp. Micro Machine Human Sci., 1995, pp. 39–43.
[10] G. Feng and G. Chen, Adaptive control of discrete-time chaotic systems: a fuzzy control approach, Chaos Solitons Fractals 23 (2005), 459–467.
[11] T.A. Gennarelli, L.E. Thibault, R. Tipperman, G. Tomei, R. Sergot, M. Brown, W.L. Maxwell, D.I. Graham, J.H. Adams, A. Irvine and L.M. Gennarelli, Axonal injury in the optic nerve: a model simulating diffuse axonal injury in the brain, J. Neurosurgery 71 (1989), no. 2, 244–253.
[12] A. Kazemi, R. Behinfaraz and A. Rikhtegar Ghiasi, Accurate model reduction of large scale systems using adaptive multi-objective particle swarm optimization algorithm, Int. Conf. Mech. Syst. Control Engin. (ICMSC), IEEE, 2017, pp. 372–376.
[13] J.P. Keener, F.C. Hoppensteadt and J. Rinzel, Integrate-and-fire models of nerve membrane response to oscillatory input, SIAM J. Appl. Math. 41 (1981), no. 3, 503–517.
[14] S. Kumar, A.E. Matouk, H. Chaudhary and S. Kant, Control and synchronization of fractional-order chaotic satellite systems using feedback and adaptive control techniques, Int. J Adaptive Control Signal Process. 35 (2021), no. 4, 484–497.
[15] C.L. Kuo, T.H. Li and N. Guo, Design of a novel fuzzy sliding-mode control for magnetic ball levitation system, J. Intell. Robotic Syst. 42 (2005), no. 3, 295–316.
[16] C. Li, X. Liao and J. Yu, Synchronization of fractional order chaotic systems, Phys. Rev. E. 68 (2003), no. 6, 067203.
[17] G. Peng, Synchronization of fractional order chaotic systems, Phys. Lett. A. 363 (2007), no. 5-6, 426–432.
[18] K. Tanaka, T. Ikeda and H.O. Wang, A unified approach to controlling chaos via LMI-based fuzzy control system design, IEEE Trans. Circuits Syst. I: Fund. Theory Appl. 45 (1998), no. 10, 1021–1040.
[19] H. Wang, Z. Han, W. Zhang and Q. Xie, Chaotic synchronization and secure communication based on descriptor observer, Nonlinear Dyn. 57 (2009), 69–73.
[20] X. Wu, H. Bao and J. Cao, Finite-time inter-layer projective synchronization of Caputo fractional-order two-layer networks by sliding mode control, J. Franklin Instit. 358 (2021), no. 1, 1002–1020.
[21] Y.J. Xue and S.Y. Yang, Synchronization of generalized Henon map by using adaptive fuzzy controller, Chaos Solitons Fractals 17 (2003), no. 4, 717–722.
[22] R.R. Yager and L.A. Zadeh, An introduction to Fuzzy logic applications in intelligent systems, Springer US, 1992.
[23] L.A. Zadeh, Fuzzy logic, IEEE Comput. 21 (1988), no. 4, 83–93.
[24] P. Zhou and W. Zhu, Function projective synchronization for fractional-order chaotic systems, Nonlinear Anal.: Real World Appl. 12 (2011), no. 2, 811–816.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 3037-3043
  • Receive Date: 26 January 2022
  • Revise Date: 23 May 2022
  • Accept Date: 19 June 2022