PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Synchronization of neuronal bursting using backstepping control with recursive feedback

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
J. L. Hindmarsh, R. M. Rose introduced the concept of neuronal burst. In this paper, synchronization is investigated for the construction of a model of neuronal burst using backstepping control with recursive feedback. Synchronization for a model of neuronal bursting system is established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of a Lyapunov function with the design of a controller. The backstepping control method is effective and convenient to synchronize identical systems. Numerical simulations are furnished to illustrate and validate the synchronization result derived in this paper.
Rocznik
Strony
617--642
Opis fizyczny
Bibliogr. 50 poz., rys., wykr., wzory
Twórcy
  • Department of Mathematics, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Tamil Nadu, Chennai-600 062, India
Bibliografia
  • [1] Qingkai Han, LinaHao, Hao Zhang and Bangchun Wen: Achivement of chaotic synchronization trajectrories of masterslave manipulators with feedback control strategy. Acta Mech. Sin., 26 (2010), 433–439.
  • [2] G. M. Mahmoud, T. Bountis, G. M. AbdEI-Latif and E. E. Mahmoud: Chaos synchronization of two different chaotic complex Chen and Lu systems. Nonlinear Dyn., 55 (2009), 43–53.
  • [3] Hamid Reza Karimi and Huijun Gao: LMI based H1 synchronization of second order neutral master-slave system using delayed output feedback control. International Journal of Control, Automation and Systems, 7 (2009), 371–380.
  • [4] Chaio-Shiung Chen and Heng-Hui Chen: Intelligent quadratic optimal synchronization of uncertain chaotic system via LMI approach. Nonlinear Dyn., 63 (2011), 171–181.
  • [5] Wangli He and Jinde Cao: Exponential synchronization of chaotic neural networks: a matrix measure approach, Nonlinear Dyn., 55 (2009), 55–65.
  • [6] Wu Xiao-qun and Lu Jun-an: Synchronization of unified chaotic system using occasional driving, Wuhan University Wuhan Univ. J. of Nat. Sci., 8 (2003), 808–812.
  • [7] K. Murali and M. Lakshmanan: Secure communication using a compound signal using sampled-data feedback, Applied Mathematics and Mechanics, 11 (2003), 1309–1315.
  • [8] T. Yang and L. O. Chua: Generalized synchronization of chaos via linear transformations. Internat. J. Bifur. Chaos, Vol. 9 (1999), 215–219.
  • [9] K. Murali and M. Lakshmanan: Chaos in Nonlinear Oscillators: Controlling and Synchronization, Singapore: World Scientific (1996).
  • [10] S. K. Han, C. Kerrer and Y. Kuramoto: D-phasing and bursting in coupled neural oscillators. Phys. Rev. Lett., 75 (1995), 3190–3193.
  • [11] B. Blasius, A. Huppert and L. Stone: Complex dynamics and phase synchronization in spatially extended ecological system. Nature, 399 (1999), 354–359.
  • [12] L. Kocarev and U. Parlitz: General approach for chaotic synchronization with applications to communications. Phys. Rev. Lett., 74 (1995), 5028–5030.
  • [13] Zuolei Wang: Chaos synchronization of an energy resource system based on linear control. Nonlinear Analysis: Realworld Application, 11(5), (2010), 3336–3343.
  • [14] Jiang Wang, Lisong Chen and Bin Deng: Synchronization of ghostburster neurons in external electrical stimulation via H1 variable universe fuzzy adaptive control. Chaos, Solitons and Fractals, 39 (2009), 2076–2085.
  • [15] Moukam Kakmeni, F. M., Nguenang, J. P. and Kofane, T. C.: Chaos synchronization in bi-axial magnets modeled by bloch equation. Chaos, Solitons and Fractals, Vol. 30, pp. 690–699, (2006).
  • [16] J. L. Hindmarsh and R. M. Rose: A model of neuronal bursting using 3-coupled first order differential equations. Proc. Roy. Soc. Lond. B. Biol, 221 (1984), 81–102.
  • [17] Yan-Qiu Che, Jiang Wang, Kai-Ming Tsang and Wai-Lok Chen: Unidirectional synchronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control. Nonlinear Analysis: Real world Application, 11 (2010), 1096–1104.
  • [18] Guang Zhao Zeng, Lan Sun Chen and Li Hua Sun: Complexity of an SIR epidemic dynamics model with impulsive vaccination control. Chaos, Solitons and Fractals, 26 (2005), 495–505.
  • [19] Junxa Wang, Dianchen Lu and Lixin Tian: Global synchronization for time delay WINDMI system. Chaos, Solitons and Fractals, 30 (2006), 629–635.
  • [20] Lin Pan, Wuneng, Jianan Fang and Dequan Li: A novel active pinning control for synchronization and antisynchronization of new uncertain unified chaotic systems. Nonlinear Dyn., 62 (2010), 417–425.
  • [21] Xuerong Shi and Zuolei Wang: Robust chaos synchronization of four dimensional energy resource system via adaptive feedback control. Nonlinear Dyn., 60(4) (2010), 631–637.
  • [22] Quanxin Zhu and Jinde Cao: Adaptive synchronization of chaotic cohen-crossberg neural networks with mixed time delays. Nonlinear Dyn., 61 (2010), 517–534.
  • [23] Jiakun Zhao and Tao Ren: Q-S synchronization between chaotic systems with double scalling functions. Nonlinear Dyn., 62 (2010), 665–672.
  • [24] Haozhou Zheng, Jinfeng Hu, PengWu, Lidong Liu and Zishu He: Study on synchronization and parameters in sensitivity of a class of hyperchaotic systems using nonlinear feedback control. Nonlinear Dyn., 67(2) (2012), 1515–1523.
  • [25] S. Bowong and J. J. Tewa: Practical adaptive synchronization of a class of uncertain chaotic system. Nonlinear Dyn., 56 (2009), 57–68.
  • [26] M. Arefi and M. R. Jahed-Motlogh: Robust synchronization of Rossler systems with mismatched time-varying parameters. Nonlinear Dyn., 67(2) (2012), 1233–1245.
  • [27] Choon Ki Ahn: Neural network H1 chaos synchronization. Nonlinear Dyn., 60 (2010), 295–302.
  • [28] Wei-Sheng Chen, Rui-Hong Li and Jing Li: Observer-based adaptive iterative learning control for nonlinear systems with time varying delays. Int. Journal of Automation and Computing, 7 (2010), 438–446.
  • [29] H. Adloo, N. Noroozi and P. Karimaghaee: Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity. Nonlinear Dyn., 67(2) (2012), 1337–1356.
  • [30] Abdurahman Kadir, Xing-Yuan Wang and Yu-Zhang Zhao: Robust adaptive fuzzy neural tracking control for a class of unknown chaotic systems. PRAMANA – Journal of Physics, 76 (2011), 887–900.
  • [31] S. Bowong: Adaptive synchronization of chaotic systems with unknown bounded uncertainities via backstepping approach. Nonlinear Dyn., 49 (2007), 59–70.
  • [32] Lu Ling, Li Yi and Guo ZhiAn: Parameter identification and synchronization of spatiotemporal chaos inan uncertain Gray-scott system. Science in China Series G: Physics, Mechanics, 51 (2008), 1638–1646.
  • [33] Jianxiong Zhang and Wanstieng Tang: Control and synchronization for a class of new chaotic systems via linear feedback. Nonlinear Dyn., 58 (2009), 675–686.
  • [34] Zuo Lei Wang and Xue Rong Shi: Adaptive Q-S synchronization of nonidentical chaotic systems with unknown parameters. Nonlinear Dyn., 59 (2010), 559–567.
  • [35] Chi-Ching Yang: Adaptive synchronization of Lu hyperchaotic system with uncertain parameters based on single input controller. Nonlinear Dyn., 63 (2010), 447–454.
  • [36] Di-Yi Chen, Lin Shi, Hai-Tao Chen and Xiao-Yi Ma: Analysis and control of a hyperchaotic system with only one nonlinear term. Nonlinear Dyn., 67(3) (2012), 1745–1752.
  • [37] Xiang-Jon Wu and Hong-Tao Lu: Generalized projective log synchronization between different hyperchaotic systems with uncertain parameters. Nonlinear Dyn., 66(1-2) (2011), 185–200.
  • [38] Chunali Mu, Fuchen Zhang, Yonglu Shu and Shouming Zhou: On the boundedness of solutions to the Lorenz-like family of chaotic systems. Nonlinear Dyn., 67(2) (2012), 987–996.
  • [39] V. Nenadovic, R. Whitney, J. Boulet and M. A. Cortez: Hypsarrhythmia in epileptic spasms: Synchrony in chaos. Seizure, 58 (2018), 55–61.
  • [40] L. Glass, M. R. Guevara and A. Shrier: Bifurcation and chaos in a periodically stimulated cardiac oscillator. Physica 7D (1983), 89–101.
  • [41] M. A. Quiroz-Juarez, R. Vazquez-Medina, E. Ryzhii, M. Ryzhii and J. L. Aragon: Quasiperiodicity route to chaos in cardiac conduction model. Commun. Nonlinear Sci. Numer. Simulat., 42 (2017), 370–378.
  • [42] Somayeh Raiesdana and S. Mohammad Hashemi Goplayegani: Study on chaos anti-control for hippocampal models of epilepsy. Neurocomputing, 111 (2013), 54–69.
  • [43] F. M. de Paula Neto, W. R. de Oliveira, T. B. Ludermir and A. J. da Silva: Chaos in a quantum neuron: an open system approach. Neurocomputing (2017), doi: 10.1016/j.neucom.2016.06.081.
  • [44] U. E. Kocamaz, H. Tapkyn, Y. Uyaroolu and A. Goksu: Control and Synchronization of Chaotic Supply Chains using Intelligent Approaches. Computers & Industrial Engineering (2016), doi: http://dx.doi.org/10.1016/j.cie.2016.03.014
  • [45] Quan Zhou, Wei Zhang, Scott Cash, Oluremi Olatunbosun, Hong-ming Xu and Guoxiang Lu: Intelligent sizing of a series hybrid electric power-train system based on Chaos-enhanced accelerated particle swarm optimization. Applied Energy, 189 (2017), 588–601.
  • [46] Yimin Yang, Yaonan Wang, Xiaofang Yuan and Feng Yin: Hybrid chaos optimization algorithm with artificial emotion. Applied Mathematics and Computation, 218 (2012), 6585–6611.
  • [47] U. E. Vincent, R. K. Odunaike, J. A. Laoye and A. A. Gbindinniuola: Adaptive backstepping control and synchronization of a modified and chaotic van der pol duffing oscillator. Journal Control Theory Application, 9 (2011), 273–271.
  • [48] J. L. Hindmarsh and R. M. Rose: A model of the nerve impulse using two first order differential equations. Nature, 296 (1982), 162–164.
  • [49] J. L. Hindmarsh and R. M. Rose: A model of neuronal bursting using three coupled first order differential equations. Proceeding of the Royal Society B, 221 (1984), 87–102.
  • [50] W. Hahn: The Stability of Motion. Berlin, Germany: Springer-Verlag, 1967.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7416e8e4-761c-439a-a3ff-ecb8e0cadbb2
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.