Synchronization of two coupled Hindmarsh-Rose neurons

Ke Ding; Qing-Long Han

Kybernetika (2015)

  • Volume: 51, Issue: 5, page 784-799
  • ISSN: 0023-5954

Abstract

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This paper is concerned with synchronization of two coupled Hind-marsh-Rose (HR) neurons. Two synchronization criteria are derived by using nonlinear feedback control and linear feedback control, respectively. A synchronization criterion for FitzHugh-Nagumo (FHN) neurons is derived as the application of control method of this paper. Compared with some existing synchronization results for chaotic systems, the contribution of this paper is that feedback gains are only dependent on system parameters, rather than dependent on the norm bounds of state variables of uncontrolled and controlled HR neurons. The effectiveness of our results are demonstrated by two simulation examples.

How to cite

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Ding, Ke, and Han, Qing-Long. "Synchronization of two coupled Hindmarsh-Rose neurons." Kybernetika 51.5 (2015): 784-799. <http://eudml.org/doc/276047>.

@article{Ding2015,
abstract = {This paper is concerned with synchronization of two coupled Hind-marsh-Rose (HR) neurons. Two synchronization criteria are derived by using nonlinear feedback control and linear feedback control, respectively. A synchronization criterion for FitzHugh-Nagumo (FHN) neurons is derived as the application of control method of this paper. Compared with some existing synchronization results for chaotic systems, the contribution of this paper is that feedback gains are only dependent on system parameters, rather than dependent on the norm bounds of state variables of uncontrolled and controlled HR neurons. The effectiveness of our results are demonstrated by two simulation examples.},
author = {Ding, Ke, Han, Qing-Long},
journal = {Kybernetika},
keywords = {coupled neurons; Hindmarsh–Rose neurons; synchronization; feedback control},
language = {eng},
number = {5},
pages = {784-799},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Synchronization of two coupled Hindmarsh-Rose neurons},
url = {http://eudml.org/doc/276047},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Ding, Ke
AU - Han, Qing-Long
TI - Synchronization of two coupled Hindmarsh-Rose neurons
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 784
EP - 799
AB - This paper is concerned with synchronization of two coupled Hind-marsh-Rose (HR) neurons. Two synchronization criteria are derived by using nonlinear feedback control and linear feedback control, respectively. A synchronization criterion for FitzHugh-Nagumo (FHN) neurons is derived as the application of control method of this paper. Compared with some existing synchronization results for chaotic systems, the contribution of this paper is that feedback gains are only dependent on system parameters, rather than dependent on the norm bounds of state variables of uncontrolled and controlled HR neurons. The effectiveness of our results are demonstrated by two simulation examples.
LA - eng
KW - coupled neurons; Hindmarsh–Rose neurons; synchronization; feedback control
UR - http://eudml.org/doc/276047
ER -

References

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  1. Barrio, R., Martinez, M. A., Serrano, S., Shilnikov, A., 10.1063/1.4882171, Chaos 24 (2014), 023128. MR3403326DOI10.1063/1.4882171
  2. Chalike, S. K., Lee, K. W., Singh, S. N., 10.1007/s11071-014-1454-6, Nonlinear Dynam. 78 (2014), 467-483. MR3266456DOI10.1007/s11071-014-1454-6
  3. Checco, P., Righero, M., Biey, M., Kocarev, L., 10.1109/tcsii.2008.2008057, IEEE Trans. Circuits Syst. II: Exp. Briefs 55 (2008), 1274-1278. DOI10.1109/tcsii.2008.2008057
  4. Ferrari, F. A. S., Viana, R. L., Lopesa, S. R., Stoop, R., 10.1016/j.neunet.2015.03.003, Neural Netw. 66 (2015), 107-118. DOI10.1016/j.neunet.2015.03.003
  5. Hindmarsh, J. L., Rose, R. M., 10.1038/296162a0, Nature 296 (1982), 162-164. DOI10.1038/296162a0
  6. Holden, A. V., Fan, Y. S., 10.1016/0960-0779(92)90032-i, Chaos Soliton Fract. 2 (1992), 221-236. Zbl0766.92006DOI10.1016/0960-0779(92)90032-i
  7. Hosaka, R., Sakai, Y., Aihara, K., 10.1007/978-3-642-10684-2_45, Lect. Notes Comput. Sci. 5864 (2009), 401-408. DOI10.1007/978-3-642-10684-2_45
  8. Hrg, D., 10.1016/j.neunet.2012.12.010, Neural Netw. 40 (2013), 73-79. Zbl1283.92017DOI10.1016/j.neunet.2012.12.010
  9. Khalil, H. K., Nonlinear Systems. Third edition., Prentice Hall, Upper Saddle River 2002. 
  10. Kuntanapreeda, S., 10.1016/j.physleta.2009.06.006, Phys. Lett. A 373 (2009), 2837-2840. Zbl1233.93047DOI10.1016/j.physleta.2009.06.006
  11. Li, H. Y., Hu, Y. A., Wang, R. Q., Adaptive finite-time synchronization of cross-strict feedback hyperchaotic systems with parameter uncertainties., Kybernetika 49 (2013), 554-567. MR3117914
  12. Li, R., He, Z., 10.1007/s11071-013-1161-8, Nonlinear Dynam. 76 (2014), 697-715. Zbl1319.37024MR3189203DOI10.1007/s11071-013-1161-8
  13. Liang, H., Wang, Z., Yue, Z., Lu, R., Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication., Kybernetika 48 (2012), 190-205. Zbl1256.93084MR2954320
  14. Liu, X., Liu, S., 10.1007/s11071-011-0030-6, Nonlinear Dynam. 67 (2012), 847-857. Zbl1245.34047MR2869243DOI10.1007/s11071-011-0030-6
  15. Lü, J., Zhou, T., Chen, G., Yang, X., 10.1063/1.1478079, Chaos 12 (2002), 344-349. DOI10.1063/1.1478079
  16. Ma, M. H., Zhang, H., Cai, J. P., Zhou, J., Impulsive practical synchronization of n-dimensional nonautonomous systems with parameter mismatch., Kybernetika 49 (2013), 539-553. Zbl1274.70039MR3117913
  17. Meyer, T., Walker, C., Cho, R. Y., Olson, C. R., 10.1038/nn.3794, Nat. Neurosci. 17 (2014), 1388-1394. DOI10.1038/nn.3794
  18. Nguyena, L. H., Hong, K. S., 10.1016/j.matcom.2011.10.005, Math. Comput. Simulations 82 (2011), 590-603. MR2877386DOI10.1016/j.matcom.2011.10.005
  19. Pecora, L. M., Carroll, T. L., 10.1103/physrevlett.64.821, Phys. Rev. Lett. 64 (1990), 821-824. MR1038263DOI10.1103/physrevlett.64.821
  20. Sadeghi, S., Valizadeh, A., 10.1007/s10827-013-0461-9, J. Comput. Neurosci. 36 (2014), 55-66. MR3160746DOI10.1007/s10827-013-0461-9
  21. Sedov, A. S., Medvednik, R. S., Raeva, S. N., 10.1134/s0362119714010137, Hum. Physiol. 40 (2014), 1-7. DOI10.1134/s0362119714010137
  22. Shen, C. W., Yu, S. M., Lu, J. H., Chen, G. R., 10.1109/tcsi.2013.2283994, IEEE Trans. Circuits Syst. I: Reg. Papers 61 (2014), 854-864. DOI10.1109/tcsi.2013.2283994
  23. Shen, C. W., Yu, S. M., Lu, J. H., Chen, G. R., 10.1109/tcsi.2014.2304655, IEEE Trans. Circuits Syst. I: Reg. Papers 61 (2014), 2380-2389. DOI10.1109/tcsi.2014.2304655
  24. Tan, X. H., Zhang, J. Y., Yang, Y. R., 10.1016/s0960-0779(02)00153-4, Chaos Soliton Fract. 16 (2003), 37-45. Zbl1035.34025MR1941155DOI10.1016/s0960-0779(02)00153-4
  25. Wang, J. G., Cai, J. P., Ma, M. H., Feng, J. C., Synchronization with error bound of non-identical forced oscillators., Kybernetika 44 (2008), 534-545. Zbl1173.70009MR2459071
  26. Wang, Q., Lu, Q., Chen, G., Guo, D., 10.1016/j.physleta.2006.03.017, Phys. Lett. A 356 (2006), 17-25. DOI10.1016/j.physleta.2006.03.017
  27. Wang, C. N., Ma, J., Tang, J., Li, Y. L., 10.1088/0253-6102/53/2/32, Commun. Theor. Phys. 53 (2010), 382-388. DOI10.1088/0253-6102/53/2/32
  28. Wei, Z., Wang, Z., Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium., Kybernetika 49 (2013), 359-374. Zbl1276.34043MR3085401
  29. Wu, X. F., Zhao, Y., Wang, M. H., Global synchronization of chaotic Lur'e systems via replacing variables control., Kybernetika 44 (2008), 571-584. Zbl1175.37040MR2459074
  30. Wu, A. L., Zeng, Z. G., 10.1016/j.neunet.2013.09.002, Neural Netw. 49 (2014), 11-18. Zbl1296.93153DOI10.1016/j.neunet.2013.09.002

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