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Volumn 69, Issue 4, 2012, Pages 2169-2179

Simulating the electric activity of FitzHugh-Nagumo neuron by using Josephson junction model

Author keywords

FitzHugh Nagumo; Generalized synchronization; Josephson junction; Power consumption

Indexed keywords

ADAPTIVE SYNCHRONIZATIONS; COMPLETE SYNCHRONIZATION; DIMENSIONLESS MODELS; DYNAMICAL PROPERTIES; ELECTRIC ACTIVITY; ERROR FUNCTION; FITZHUGH- NAGUMO; FITZHUGH-NAGUMO SYSTEMS; GAIN COEFFICIENTS; GENERALIZED SYNCHRONIZATION; JOSEPHSON JUNCTIONS; LINEAR GENERALIZED SYNCHRONIZATIONS; PHASE SPACES;

EID: 84866139490     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0417-z     Document Type: Article
Times cited : (41)

References (40)
  • 1
    • 0008161311 scopus 로고
    • Effect of ac impedance on dc voltagecurrent characteristics of superconductor weak-link junction
    • McCumber, D.E.: Effect of ac impedance on dc voltagecurrent characteristics of superconductor weak-link junction. J. Appl. Phys. 39, 3113 (1968)
    • (1968) J. Appl. Phys. , vol.39 , pp. 3113
    • McCumber, D.E.1
  • 2
    • 0003855865 scopus 로고
    • Effect of inductance on externally shunted Josephson tunnel junctions
    • Whan, C.B., Lobb, C.J., Forrester, M.G.: Effect of inductance on externally shunted Josephson tunnel junctions. J. Appl. Phys. 77, 382 (1995)
    • (1995) J. Appl. Phys. , vol.77 , pp. 382
    • Whan, C.B.1    Lobb, C.J.2    Forrester, M.G.3
  • 3
    • 0003731567 scopus 로고    scopus 로고
    • Complex dynamical behavior in RCL-shunted josephson tunnel junctions
    • Whan, C.B., Lobb, C.J.: Complex dynamical behavior in RCL-shunted josephson tunnel junctions. Phys. Rev. E 53, 405 (1996)
    • (1996) Phys. Rev. E , vol.53 , pp. 405
    • Whan, C.B.1    Lobb, C.J.2
  • 5
    • 44449090893 scopus 로고    scopus 로고
    • Electromagnetic waves in single-and multi-josephson junctions
    • Supercond.
    • Matsumoto, H., Koyama, T., Machida, M., et al.: Electromagnetic waves in single-and multi-Josephson junctions. Physica C, Supercond. 468, 654-659 (2008)
    • (2008) Physica C , vol.468 , pp. 654-659
    • Matsumoto, H.1    Koyama, T.2    Machida, M.3
  • 6
    • 63849333691 scopus 로고    scopus 로고
    • Mechanism of terahertz electromagnetic wave emission from intrinsic Josephson junctions
    • Tachiki, M., Fukuya, S., Koyama, T., et al.: Mechanism of terahertz electromagnetic wave emission from intrinsic Josephson junctions. Phys. Rev. Lett. 102, 1270021 (2009)
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 1270021
    • Tachiki, M.1    Fukuya, S.2    Koyama, T.3
  • 7
    • 67649433210 scopus 로고    scopus 로고
    • Chaos in Josephson junctions and its application in secure communications
    • Zhou, T.G., Mao, J., Liu, T.S., et al.: Chaos in Josephson junctions and its application in secure communications. Cryog. & Supercond. 4, 1-5 (2009)
    • (2009) Cryog. & Supercond. , vol.4 , pp. 1-5
    • Zhou, T.G.1    Mao, J.2    Liu, T.S.3
  • 8
    • 37149011219 scopus 로고    scopus 로고
    • The model of capacitive coupled intrinsic Josephson junction array and its chaotic behavior
    • in Chinese
    • Zhou, T.G., Song, F.B., Fang, L., et al.: The model of capacitive coupled intrinsic Josephson junction array and its chaotic behavior. Acta Phys. Sin. 11, 6307-6313 (2007) (in Chinese)
    • (2007) Acta Phys. Sin. , vol.11 , pp. 6307-6313
    • Zhou, T.G.1    Song, F.B.2    Fang, L.3
  • 9
    • 84855277497 scopus 로고    scopus 로고
    • Synchronization of coupled chaotic Fitz Hugh-Nagumo neurons via Lyapunov functions
    • doi:10.1016/j.matcom.2011.10.005
    • Nguyena, L.H., Hong, K.S.: Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions. Math. Comput. Simulat. (2011). doi:10.1016/j.matcom.2011.10.005
    • (2011) Math. Comput. Simulat.
    • Nguyena, L.H.1    Hong, K.S.2
  • 10
    • 33745840553 scopus 로고    scopus 로고
    • Chaos synchronization in RCL-shunted Josephson junction via active control
    • DOI 10.1016/j.chaos.2005.09.035, PII S0960077905008878
    • Ucar, A., Lonngren, K.E., Bai, E.W., et al.: Chaos synchronization in RCL-shunted Josephson junction via active controller. Chaos Solitons Fractals 3, 105-111 (2007) (Pubitemid 44038544)
    • (2007) Chaos, Solitons and Fractals , vol.31 , Issue.1 , pp. 105-111
    • Ucar, A.1    Lonngren, K.E.2    Bai, E.-W.3
  • 11
    • 66149136520 scopus 로고    scopus 로고
    • Synchronization of chaos in RCL-shunted Josephson junction using a simple adaptive controller
    • Guo, R., Vincent, U.E., Idowu, B.A., et al.: Synchronization of chaos in RCL-shunted Josephson junction using a simple adaptive controller. Phys. Scr. 79, 1-5 (2008)
    • (2008) Phys. Scr. , vol.79 , pp. 1-5
    • Guo, R.1    Vincent, U.E.2    Idowu, B.A.3
  • 12
    • 66349094021 scopus 로고    scopus 로고
    • Influence of Josephson junction parameters on Shapiro steps
    • (in Chinese
    • Liu, F.L., Zhou, T.G., Wang, D.C., et al.: Influence of Josephson junction parameters on Shapiro steps. Acta Electron. Sin. 5, 957-959 (2009) (in Chinese)
    • (2009) Acta Electron. Sin. , vol.5 , pp. 957-959
    • Liu, F.L.1    Zhou, T.G.2    Wang, D.C.3
  • 13
    • 77954819904 scopus 로고    scopus 로고
    • Josephson junction simulation of neurons
    • Crotty, P., Schult, D., Segall, K., et al.: Josephson junction simulation of neurons. Phys. Rev. E 82, 0119141 (2010)
    • (2010) Phys. Rev. E , vol.82 , pp. 0119141
    • Crotty, P.1    Schult, D.2    Segall, K.3
  • 14
    • 0033363928 scopus 로고    scopus 로고
    • How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate
    • DOI 10.1038/9173
    • Stemmler, M., Koch, C.: How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate. Nat. Neurosci. 6, 521-527 (1999) (Pubitemid 30491232)
    • (1999) Nature Neuroscience , vol.2 , Issue.6 , pp. 521-527
    • Stemmler, M.1    Koch, C.2
  • 15
    • 69249209629 scopus 로고    scopus 로고
    • Chaotic bursting lag synchronization of hindmarsh-Rose system via a single controller
    • Wang, Z.L., Shi, X.R.: Chaotic bursting lag synchronization of Hindmarsh-Rose system via a single controller. Appl. Math. Comput. 3, 1091-1097 (2009)
    • (2009) Appl. Math. Comput. , vol.3 , pp. 1091-1097
    • Wang, Z.L.1    Shi, X.R.2
  • 16
    • 77955775947 scopus 로고    scopus 로고
    • Limit dynamics for the stochastic fitzhugh-Nagumo system
    • Wang, Y.L.: Limit dynamics for the stochastic FitzHugh-Nagumo system. Nonlinear Anal., Real World Appl. 4, 3091-3105 (2010)
    • (2010) Nonlinear Anal., Real World Appl. , vol.4 , pp. 3091-3105
    • Wang, Y.L.1
  • 17
    • 53349102813 scopus 로고
    • The biophysical society all rights reserved
    • FitzHugh, R.: The biophysical society all rights reserved. Biophys. J. 1, 445-466 (1961)
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • FitzHugh, R.1
  • 18
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • Nagumo, J., Arimoto, S., Yoshizawa, S., et al.: An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061-2070 (1962)
    • (1962) Proc. IRE , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 19
    • 84866127124 scopus 로고    scopus 로고
    • Synchronization properties of coupled Fitz Hugh-Nagumo systems
    • In: Mallamace, F., Stanley, H.E. (eds.), Course CLV: The Physics of Complex Systems (New Advances and Perspectives IOS Press, Amsterdam
    • Tessone, C.J., Toral, R., Mirasso, C.R., et al.: Synchronization properties of coupled FitzHugh-Nagumo systems. In: Mallamace, F., Stanley, H.E. (eds.) Pro. Int School Phys. Enrico Fermi, Course CLV: The Physics of Complex Systems (New Advances and Perspectives), p. 461. IOS Press, Amsterdam (2004)
    • (2004) Pro. Int School Phys. Enrico Fermi , vol.461
    • Tessone, C.J.1    Toral, R.2    Mirasso, C.R.3
  • 20
    • 0000455922 scopus 로고    scopus 로고
    • Bursting behaviour of the FitzHugh-Nagumo neuron model subject to quasi-monochromatic noise
    • PII S0167278998001766
    • Baltanás, J.P., Casado, J.M.: Bursting behaviour of the FitzHugh-Nagumo neuron model subject to quasimonochromatic noise. Physica D 122, 231-240 (1998) (Pubitemid 128636773)
    • (1998) Physica D: Nonlinear Phenomena , vol.122 , Issue.1-4 , pp. 231-240
    • Baltanas, J.P.1    Casado, J.M.2
  • 21
    • 0035424393 scopus 로고    scopus 로고
    • The role of synaptic coupling in a network of FHN neuron models
    • DOI 10.1016/S0362-546X(01)00342-X, PII S0362546X0100342X
    • Chillemi, S., Barbi, M., Garbo, A.D., et al.: The role of synaptic coupling in a network of FHN neuron models. Nonlinear Anal. 3, 2163-2169 (2001) (Pubitemid 32733098)
    • (2001) Nonlinear Analysis, Theory, Methods and Applications , vol.47 , Issue.3 , pp. 2163-2169
    • Chillemi, S.1    Barbi, M.2    Di Garbo, A.3
  • 22
    • 62549098158 scopus 로고    scopus 로고
    • Bifurcation and synchronization of synoptically coupled FHN models with time delay
    • Wang, Q.Y., Lu, Q.S., Chen, G.R., et al.: Bifurcation and synchronization of synoptically coupled FHN models with time delay. Chaos Solitons Fractals 2, 918-925 (2009)
    • (2009) Chaos Solitons Fractals , vol.2 , pp. 918-925
    • Wang, Q.Y.1    Lu, Q.S.2    Chen, G.R.3
  • 23
    • 69049107414 scopus 로고    scopus 로고
    • Bautin bifurcation analysis for synchronous solution of a coupled FHN neural system with delay
    • Zhen, B., Xu, J.: Bautin bifurcation analysis for synchronous solution of a coupled FHN neural system with delay. Commun. Nonlinear Sci. Numer. Simul. 2, 442-458 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.2 , pp. 442-458
    • Zhen, B.1    Xu, J.2
  • 24
    • 74449087727 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in a synaptically coupled fhn neuron with delays
    • Fan, D.J., Hong, L.: Hopf bifurcation analysis in a synaptically coupled FHN neuron with delays. Commun. Nonlinear Sci. Numer. Simul. 7, 1873-1886 (2010)
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.7 , pp. 1873-1886
    • Fan, D.J.1    Hong, L.2
  • 26
    • 84862989360 scopus 로고    scopus 로고
    • Complete dynamical analysis of a neuron model
    • doi:10.1007/s11071-011-0046-y
    • Shilnikov, A.: Complete dynamical analysis of a neuron model. Nonlinear Dyn. (2011). doi:10.1007/s11071-011-0046-y
    • (2011) Nonlinear Dyn.
    • Shilnikov, A.1
  • 28
    • 77953361931 scopus 로고    scopus 로고
    • Lag synchronization of multiple identical hindmarsh-Rose neuron models coupled in a ring structure
    • Wang, Z.L., Shi, X.R.: Lag synchronization of multiple identical Hindmarsh-Rose neuron models coupled in a ring structure. Nonlinear Dyn. 60, 375-383 (2010)
    • (2010) Nonlinear Dyn. , vol.60 , pp. 375-383
    • Wang, Z.L.1    Shi, X.R.2
  • 29
    • 84864402645 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays
    • Fan, D.J., Hong, L., Wei, J.J.: Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays. Nonlinear Dyn. 62, 305-319 (2010)
    • (2010) Nonlinear Dyn. , vol.62 , pp. 305-319
    • Fan, D.J.1    Hong, L.2    Wei, J.J.3
  • 30
    • 56749091555 scopus 로고    scopus 로고
    • Hopf bifurcation analysis of a fourneuron network with multiple time delays
    • Mao, X.C., Hu, H.Y.: Hopf bifurcation analysis of a fourneuron network with multiple time delays. Nonlinear Dyn. 55, 95-112 (2009)
    • (2009) Nonlinear Dyn. , vol.55 , pp. 95-112
    • Mao, X.C.1    Hu, H.Y.2
  • 31
    • 79051469197 scopus 로고    scopus 로고
    • Synchronization transitions on small-World neuronal networks: effects of information transmission delay and rewiring probability
    • Wang, Q.Y., Duan, Z.S., Perc, M., et al.: Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability. Europhys. Lett. 83, 50008 (2008)
    • (2008) Europhys. Lett. , vol.83 , pp. 50008
    • Wang, Q.Y.1    Duan, Z.S.2    Perc, M.3
  • 32
    • 69449089341 scopus 로고    scopus 로고
    • Synchronization transitions on scale-Free neuronal networks due to finite information transmission delays
    • Wang, Q.Y., Perc, M., Duan, Z.S., et al.: Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys. Rev. E 80, 026206 (2009)
    • (2009) Phys. Rev. E , vol.80 , pp. 026206
    • Wang, Q.Y.1    Perc, M.2    Duan, Z.S.3
  • 33
    • 77953126942 scopus 로고    scopus 로고
    • Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling
    • Wang, Q.Y., Perc, M., Duan, Z.S., et al.: Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling. Physica A 389, 3299-3306 (2010)
    • (2010) Physica A , vol.389 , pp. 3299-3306
    • Wang, Q.Y.1    Perc, M.2    Duan, Z.S.3
  • 34
    • 79251577062 scopus 로고    scopus 로고
    • Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling
    • Wang, Q.Y., Chen, G.R., Perc, M.: Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling. PLoS ONE 6, e15851 (2011)
    • (2011) PLoS ONE , vol.6
    • Wang, Q.Y.1    Chen, G.R.2    Perc, M.3
  • 35
    • 79953288977 scopus 로고    scopus 로고
    • Burst synchronization transitions in a neuronal network of subnetworks
    • Sun, X.J., Lei, J.Z., Perc, M., et al.: Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21, 016110 (2011)
    • (2011) Chaos , vol.21 , pp. 016110
    • Sun, X.J.1    Lei, J.Z.2    Perc, M.3
  • 36
    • 79955697961 scopus 로고    scopus 로고
    • Taming desynchronized bursting with delays in the Macaque cortical network
    • Wang, Q.Y., Aleksandra, M., Perc, M., et al.: Taming desynchronized bursting with delays in the Macaque cortical network. Chin. Phys. B 20, 040504 (2011)
    • (2011) Chin. Phys. B , vol.20 , pp. 040504
    • Wang, Q.Y.1    Aleksandra, M.2    Perc, M.3
  • 37
    • 84866137475 scopus 로고    scopus 로고
    • Ermentrout, B.: XPPAUT (2012). http://www.math.pitt. edu/bard/xpp/xpp. html
    • (2012) XPPAUT
    • Ermentrout, B.1
  • 38
    • 84866136958 scopus 로고    scopus 로고
    • Doedel, E.: AUTO (2012). ftp://ftp.cs.concordia.ca/pub/doedel/auto
    • (2012) AUTO
    • Doedel, E.1
  • 40
    • 84869468490 scopus 로고    scopus 로고
    • Dynamic bifurcation diagrams for some models in economics and biology
    • Thessaloniki, Greece
    • Georgescu, A.: Dynamic bifurcation diagrams for some models in economics and biology. In: Proc. Int. Confer. Theory Applicat Math. Inform -ICTAMI, Thessaloniki, Greece, pp. 156-163 (2004)
    • (2004) Proc. Int. Confer Theory Applicat Math. Inform-ICTAMI , pp. 156-163
    • Georgescu, A.1


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