메뉴 건너뛰기




Volumn 33, Issue 1, 2007, Pages 217-224

Bifurcation control of the Hodgkin-Huxley equations

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; CONTROL EQUIPMENT; MATHEMATICAL MODELS; PARAMETER ESTIMATION; VOLTAGE CONTROL;

EID: 33846827228     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.01.035     Document Type: Article
Times cited : (48)

References (29)
  • 1
    • 35649001607 scopus 로고
    • A quantitative description of membrane and its application to conduction and excitation in nerve
    • Hodgkin A.L., and Huxley A.F. A quantitative description of membrane and its application to conduction and excitation in nerve. J Physiol 117 (1952) 500-544
    • (1952) J Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 2
    • 77956707015 scopus 로고
    • Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo
    • Hodgkin A.L., and Huxley A.F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol 116 (1952) 449-472
    • (1952) J Physiol , vol.116 , pp. 449-472
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 3
    • 76949125485 scopus 로고
    • The components of membrane conductance in the giant axon of Loligo
    • Hodgkin A.L., and Huxley A.F. The components of membrane conductance in the giant axon of Loligo. J Physiol 116 (1952) 473-496
    • (1952) J Physiol , vol.116 , pp. 473-496
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 4
    • 77956677051 scopus 로고
    • The dual effect of membrane potential on sodium conductance in the giant axon of Loligo
    • Hodgkin A.L., and Huxley A.F. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J Physiol 116 (1952) 497-506
    • (1952) J Physiol , vol.116 , pp. 497-506
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 5
    • 33745862625 scopus 로고    scopus 로고
    • Feedback control of Hodgkin-Huxley nerve cell dynamics
    • Fröhlich F., and Jezernik S. Feedback control of Hodgkin-Huxley nerve cell dynamics. Control Eng Practice 10 (2004) 008-019
    • (2004) Control Eng Practice , vol.10 , pp. 008-019
    • Fröhlich, F.1    Jezernik, S.2
  • 6
    • 0000447520 scopus 로고    scopus 로고
    • Suppression and control of Epileptiform activity by electrical stimulation: a review
    • Durand D.M., and Marom B. Suppression and control of Epileptiform activity by electrical stimulation: a review. IEEE 89 7 (2001) 1065-1082
    • (2001) IEEE , vol.89 , Issue.7 , pp. 1065-1082
    • Durand, D.M.1    Marom, B.2
  • 7
    • 0034145622 scopus 로고    scopus 로고
    • Hopf bifurcation in multiple-parameter space of the Hodgkin-Huxley equations I. Global organization of bistable periodic solutions
    • Fukai H., Doi S., et al. Hopf bifurcation in multiple-parameter space of the Hodgkin-Huxley equations I. Global organization of bistable periodic solutions. Biol Cybernet 82 (2000) 215-222
    • (2000) Biol Cybernet , vol.82 , pp. 215-222
    • Fukai, H.1    Doi, S.2
  • 8
    • 0000370809 scopus 로고
    • Bifurcation of the Hodgkin-Huxley equations: a new twist
    • Guckemeimer J., and Labouriau I. Bifurcation of the Hodgkin-Huxley equations: a new twist. Bull Math Biol 55 (1993) 937-952
    • (1993) Bull Math Biol , vol.55 , pp. 937-952
    • Guckemeimer, J.1    Labouriau, I.2
  • 9
    • 22344451555 scopus 로고    scopus 로고
    • Bifurcation and chaos in discrete-time predator-prey system
    • Jing Z.J., and Yang J.P. Bifurcation and chaos in discrete-time predator-prey system. Chaos, Solitons & Fractals 27 1 (2006) 259-277
    • (2006) Chaos, Solitons & Fractals , vol.27 , Issue.1 , pp. 259-277
    • Jing, Z.J.1    Yang, J.P.2
  • 10
    • 0022661079 scopus 로고
    • Local feedback stabilization and bifurcation control. Part I: Hopf bifurcation
    • Part II: Stationary bifurcation1987;8:467-73
    • Abed E.H., and Fu J.H. Local feedback stabilization and bifurcation control. Part I: Hopf bifurcation. Sys Contr Lett 7 (1986) 11-17 Part II: Stationary bifurcation1987;8:467-73
    • (1986) Sys Contr Lett , vol.7 , pp. 11-17
    • Abed, E.H.1    Fu, J.H.2
  • 11
    • 18444362136 scopus 로고    scopus 로고
    • Multiple bifurcations and periodic bubbling in a delay population model
    • Peng M. Multiple bifurcations and periodic bubbling in a delay population model. Chaos, Solitons & Fractals 25 5 (2005) 1123-1130
    • (2005) Chaos, Solitons & Fractals , vol.25 , Issue.5 , pp. 1123-1130
    • Peng, M.1
  • 12
    • 4243110500 scopus 로고    scopus 로고
    • Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models
    • Zhang H., Ma X.-k., Xue B.-l., and Liu W.-z. Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models. Chaos, Solitons & Fractals 23 2 (2005) 431-444
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.2 , pp. 431-444
    • Zhang, H.1    Ma, X.-k.2    Xue, B.-l.3    Liu, W.-z.4
  • 13
    • 3142680394 scopus 로고    scopus 로고
    • Hopf bifurcation in a control system for the washout filter-based delayed neural equation
    • Zhou S., Liao X., Wu Z., and Wong K.-w. Hopf bifurcation in a control system for the washout filter-based delayed neural equation. Chaos, Solitons & Fractals 23 1 (2005) 101-115
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.1 , pp. 101-115
    • Zhou, S.1    Liao, X.2    Wu, Z.3    Wong, K.-w.4
  • 14
    • 0031386590 scopus 로고    scopus 로고
    • Wang HO, Chen DS, Bushnell L. Control of bifurcations and chaos in heart rhythms. Proc 36th IEEE conf on decision and control, 1997. p. 395-400.
  • 15
    • 0031258280 scopus 로고    scopus 로고
    • Bifurcation control of two nonlinear models of cardiac activity
    • Brandt M.E., and Chen G. Bifurcation control of two nonlinear models of cardiac activity. IEEE Trans Circ Syst I 44 (1997) 1031-1034
    • (1997) IEEE Trans Circ Syst I , vol.44 , pp. 1031-1034
    • Brandt, M.E.1    Chen, G.2
  • 16
    • 0032642505 scopus 로고    scopus 로고
    • On time-delayed feedback control of chaotic dynamical systems
    • Chen G., and Yu X. On time-delayed feedback control of chaotic dynamical systems. IEEE Trans Circ Syst I 46 (1999) 767-772
    • (1999) IEEE Trans Circ Syst I , vol.46 , pp. 767-772
    • Chen, G.1    Yu, X.2
  • 17
    • 0000543326 scopus 로고
    • Stabilization of period doubling bifurcations and implications for control of chaos
    • Abed E.H., Wang H.O., and Chen R.C. Stabilization of period doubling bifurcations and implications for control of chaos. Physica D 70 (1994) 154-164
    • (1994) Physica D , vol.70 , pp. 154-164
    • Abed, E.H.1    Wang, H.O.2    Chen, R.C.3
  • 18
    • 0029376196 scopus 로고
    • Bifurcation control of a chaotic system
    • Wang H.O., and Abed E.H. Bifurcation control of a chaotic system. Automatica 31 (1995) 1213-1226
    • (1995) Automatica , vol.31 , pp. 1213-1226
    • Wang, H.O.1    Abed, E.H.2
  • 19
    • 0032304717 scopus 로고    scopus 로고
    • Feedback control of limit cycle amplitudes from a frequency domain approach
    • Berns D.W., Moiola J.L., and Chen G. Feedback control of limit cycle amplitudes from a frequency domain approach. Automatica 34 (1998) 1567-1573
    • (1998) Automatica , vol.34 , pp. 1567-1573
    • Berns, D.W.1    Moiola, J.L.2    Chen, G.3
  • 20
    • 0031676701 scopus 로고    scopus 로고
    • Bifurcation and normal form of nonlinear control systems, Parts I and II
    • Kang W. Bifurcation and normal form of nonlinear control systems, Parts I and II. SIAM J Contr Optim 36 (1998) 193-232
    • (1998) SIAM J Contr Optim , vol.36 , pp. 193-232
    • Kang, W.1
  • 21
    • 0034439695 scopus 로고    scopus 로고
    • Wang HO, Chen DS, Bushnell L. Dynamic feedback control of bifurcations. In: Proc 39th IEEE conf on decision and control, 2000. p. 1619-24.
  • 22
    • 19144372247 scopus 로고    scopus 로고
    • Multi-parameter Hopf-bifurcation in Hodgkin-Huxley model exposed to ELF external electric field
    • Wang J., Che Y., Fei X., and Li L. Multi-parameter Hopf-bifurcation in Hodgkin-Huxley model exposed to ELF external electric field. Chaos, Solitons & Fractals 26 4 (2005) 1221-1229
    • (2005) Chaos, Solitons & Fractals , vol.26 , Issue.4 , pp. 1221-1229
    • Wang, J.1    Che, Y.2    Fei, X.3    Li, L.4
  • 23
    • 0344062649 scopus 로고    scopus 로고
    • Hopf bifurcation in the Hodgkin-Huxley model exposed to ELF electrical field
    • Wang J., Kai M.T., and Zhang H. Hopf bifurcation in the Hodgkin-Huxley model exposed to ELF electrical field. Chaos, Solitons & Fractals 20 4 (2004) 759-764
    • (2004) Chaos, Solitons & Fractals , vol.20 , Issue.4 , pp. 759-764
    • Wang, J.1    Kai, M.T.2    Zhang, H.3
  • 24
    • 19144367571 scopus 로고    scopus 로고
    • Controlling and anti-controlling Hopf bifurcations in discrete maps using polynomial functions
    • Chen Z., and Yu P. Controlling and anti-controlling Hopf bifurcations in discrete maps using polynomial functions. Chaos, Solitons & Fractals 26 4 (2005) 1231-1248
    • (2005) Chaos, Solitons & Fractals , vol.26 , Issue.4 , pp. 1231-1248
    • Chen, Z.1    Yu, P.2
  • 25
    • 0038239703 scopus 로고    scopus 로고
    • Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems
    • Luo X.S., Chen G., Wang B.H., and Fang J.Q. Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems. Chaos, Solitons & Fractals 18 4 (2003) 775-783
    • (2003) Chaos, Solitons & Fractals , vol.18 , Issue.4 , pp. 775-783
    • Luo, X.S.1    Chen, G.2    Wang, B.H.3    Fang, J.Q.4
  • 26
    • 9544252185 scopus 로고    scopus 로고
    • Controlling Hopf bifurcations of discrete-time systems in resonance
    • Wen G., Xu D., and Xie J. Controlling Hopf bifurcations of discrete-time systems in resonance. Chaos, Solitons & Fractals 23 5 (2005) 1865-1877
    • (2005) Chaos, Solitons & Fractals , vol.23 , Issue.5 , pp. 1865-1877
    • Wen, G.1    Xu, D.2    Xie, J.3
  • 27
    • 1842528950 scopus 로고    scopus 로고
    • Dynamical mechanisms for sensitive response of aperiodic firing cells to external stimulation
    • Yong X., Xu J.-X., Hu S.-J., Kang Y.-M., Yang H.-J., and Duan Y.-B. Dynamical mechanisms for sensitive response of aperiodic firing cells to external stimulation. Chaos, Solitons & Fractals 22 1 (2004) 151-160
    • (2004) Chaos, Solitons & Fractals , vol.22 , Issue.1 , pp. 151-160
    • Yong, X.1    Xu, J.-X.2    Hu, S.-J.3    Kang, Y.-M.4    Yang, H.-J.5    Duan, Y.-B.6
  • 28
    • 1642303941 scopus 로고    scopus 로고
    • Hopf bifurcation analysis of the Lü system
    • Yu Y., and Zhang S. Hopf bifurcation analysis of the Lü system. Chaos, Solitons & Fractals 21 5 (2004) 1215-1220
    • (2004) Chaos, Solitons & Fractals , vol.21 , Issue.5 , pp. 1215-1220
    • Yu, Y.1    Zhang, S.2
  • 29
    • 0035372163 scopus 로고    scopus 로고
    • Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function
    • Liao X., Wong K.-W., Leung C.-S., and Wu Z. Hopf bifurcation and chaos in a single delayed neuron equation with non-monotonic activation function. Chaos, Solitons & Fractals 12 8 (2001) 1535-1547
    • (2001) Chaos, Solitons & Fractals , vol.12 , Issue.8 , pp. 1535-1547
    • Liao, X.1    Wong, K.-W.2    Leung, C.-S.3    Wu, Z.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.