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Volumn 17, Issue 3, 2007, Pages 985-998

Bifurcations in two-dimensional Hindmarsh-rose type model

Author keywords

Bifurcation theory; Class 1 and class 2 neurons; FitzHugh nagumo model; Hindmarsh rose model; Neuronal excitability and spiking

Indexed keywords

BIFURCATION (MATHEMATICS); BIOELECTRIC POTENTIALS; FUNCTIONAL ELECTRIC STIMULATION; NEURONS; PARAMETER ESTIMATION;

EID: 34249105813     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127407017707     Document Type: Article
Times cited : (46)

References (27)
  • 2
    • 0030767180 scopus 로고    scopus 로고
    • Regulation of native Kvl.3 channels by cAMP-dependent protein phosphorylation
    • Chung, I. &. Schlichter, L. C. [1997] "Regulation of native Kvl.3 channels by cAMP-dependent protein phosphorylation," Am. J. Physiol. Cell. Physiol. 273, 622-633.
    • (1997) Am. J. Physiol. Cell. Physiol , vol.273 , pp. 622-633
    • Chung, I.1    Schlichter, L.C.2
  • 3
    • 0017353458 scopus 로고
    • Neural repetitive firing: Modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons
    • Connor, J. A., Walter, D. & McKown, R. [1977] "Neural repetitive firing: Modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons," Biophys. J. 18, 81-102.
    • (1977) Biophys. J , vol.18 , pp. 81-102
    • Connor, J.A.1    Walter, D.2    McKown, R.3
  • 4
    • 0003297685 scopus 로고
    • Relaxation oscillations including a standard chase on French ducks
    • Eckhaus, W. [1983] "Relaxation oscillations including a standard chase on French ducks," Lect. Notes in Math. 985, 449-494.
    • (1983) Lect. Notes in Math , vol.985 , pp. 449-494
    • Eckhaus, W.1
  • 5
    • 0030195232 scopus 로고    scopus 로고
    • Type I membranes, phase resetting curves and synchrony
    • Ermentrout, G. B. [1996] "Type I membranes, phase resetting curves and synchrony," Neural Comput. 8, 979-1001.
    • (1996) Neural Comput , vol.8 , pp. 979-1001
    • Ermentrout, G.B.1
  • 6
    • 53349102813 scopus 로고
    • Impulses and physiological state in theoretical models of nerve membrane
    • FitzHugh, R. [1961] "Impulses and physiological state in theoretical models of nerve membrane," Biophy. J. 1, 445-467.
    • (1961) Biophy. J , vol.1 , pp. 445-467
    • FitzHugh, R.1
  • 7
    • 21144450311 scopus 로고    scopus 로고
    • Itinerant dynamics of class I* neurons coupled by gap junctions
    • Cortical Dynamics, eds. Eŕdi, P, Esposito, A, Marinaro, M. & Scarpetta, S, Springer-Verlag, pp
    • Fujii, H. & Tsuda, I. [2004] "Itinerant dynamics of class I* neurons coupled by gap junctions," Cortical Dynamics, eds. Eŕdi, P., Esposito, A., Marinaro, M. & Scarpetta, S., Lecture Notes in Computer Science, Vol. 3146 (Springer-Verlag), pp. 140-160.
    • (2004) Lecture Notes in Computer Science , vol.3146 , pp. 140-160
    • Fujii, H.1    Tsuda, I.2
  • 8
    • 18144400379 scopus 로고    scopus 로고
    • The onset and extinction of neural spiking: A numerical bifurcation approach
    • Govaerts, W. & Sautois, B. [2005] "The onset and extinction of neural spiking: A numerical bifurcation approach," J. Comput. Neurosci. 18, 265-274.
    • (2005) J. Comput. Neurosci , vol.18 , pp. 265-274
    • Govaerts, W.1    Sautois, B.2
  • 9
    • 0020049721 scopus 로고
    • A model of the nerve impulse using two first-order differential equations
    • Hindmarsh, J. L. & Rose, R. M. [1982] "A model of the nerve impulse using two first-order differential equations," Nature 296, 162-164.
    • (1982) Nature , vol.296 , pp. 162-164
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 10
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first order differential equations
    • Hindmarsh, J. L. & Rose, R. M. [1984] "A model of neuronal bursting using three coupled first order differential equations," Philos. Trans. R. Soc. London, Ser. B 221, 87-102.
    • (1984) Philos. Trans. R. Soc. London, Ser. B , vol.221 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 11
    • 0000235969 scopus 로고
    • The local electric changes associated with repetitive action in a non-medullated axon
    • Hodgkin, A. L. [1948] "The local electric changes associated with repetitive action in a non-medullated axon," J. Physiol 107, 165-181.
    • (1948) J. Physiol , vol.107 , pp. 165-181
    • Hodgkin, A.L.1
  • 12
    • 35649001607 scopus 로고
    • A qualitative description of membrane current and its application to conduction and excitation in nerve
    • Hodgkin, A. L. & Huxley, A. F. [1952] "A qualitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. 117, 500-544.
    • (1952) J. Physiol , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 14
    • 0000303940 scopus 로고    scopus 로고
    • Neural excitability, spiking and bursting
    • Izhikevich, E. M. [2000] "Neural excitability, spiking and bursting," Int. J. Bifurcation and Chaos 10, 1171-1266.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 1171-1266
    • Izhikevich, E.M.1
  • 15
    • 4344661328 scopus 로고    scopus 로고
    • Which model to use for cortical spiking neurons?
    • Izhikevich, E. M. [2004] "Which model to use for cortical spiking neurons?" IEEE Trans. Neural Networks 15, 1063-1070.
    • (2004) IEEE Trans. Neural Networks , vol.15 , pp. 1063-1070
    • Izhikevich, E.M.1
  • 16
    • 34250112778 scopus 로고
    • On the concept of attractor
    • Milnor, J. [1985] "On the concept of attractor," Commun. Math. Phys. 99, 177-195.
    • (1985) Commun. Math. Phys , vol.99 , pp. 177-195
    • Milnor, J.1
  • 17
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnacle giant muscle fiber
    • Morris, C. & Lecar, H. [1981] "Voltage oscillations in the barnacle giant muscle fiber," Biophys. 35, 193-213.
    • (1981) Biophys , vol.35 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 19
    • 6344238035 scopus 로고
    • An active pulse transmission line simulating nerve axon
    • Nagumo, J., Arimoto, S. & Yoshizawa, S. [1962] "An active pulse transmission line simulating nerve axon," Proc. IRE 50, 2061-2070.
    • (1962) Proc. IRE , vol.50 , pp. 2061-2070
    • Nagumo, J.1    Arimoto, S.2    Yoshizawa, S.3
  • 20
    • 0002453062 scopus 로고
    • Analysis of neural excitability and oscillations
    • eds. Koch, C. & Segev, I, The MIT Press, Cambridge
    • Rinzel, J. & Ermentrout, G. B. [1989] "Analysis of neural excitability and oscillations," Methods in Neural Modeling, eds. Koch, C. & Segev, I. (The MIT Press, Cambridge).
    • (1989) Methods in Neural Modeling
    • Rinzel, J.1    Ermentrout, G.B.2
  • 21
    • 0021871062 scopus 로고
    • The A-current: How ubiquitous a feature of excitable cells is it?
    • Rogawski, M. A. [1985] "The A-current: How ubiquitous a feature of excitable cells is it?" TINS. 8, 214-219.
    • (1985) TINS , vol.8 , pp. 214-219
    • Rogawski, M.A.1
  • 22
    • 0024328728 scopus 로고
    • The assembly of ionic currents in a thalamic neuron I. The three-dimensional model
    • Rose, R. M. & Hindmarsh, J. L. [1989] "The assembly of ionic currents in a thalamic neuron I. The three-dimensional model," Proc. R. Soc. Lond. B 237, 267-288.
    • (1989) Proc. R. Soc. Lond. B , vol.237 , pp. 267-288
    • Rose, R.M.1    Hindmarsh, J.L.2
  • 23
    • 2942705976 scopus 로고    scopus 로고
    • Comparison of coding capabilities of Type I and Type II neurons
    • St-Hilaire, M. & Longtin, A. [2004] "Comparison of coding capabilities of Type I and Type II neurons," J. Comput. Neurosci. 16, 299-313.
    • (2004) J. Comput. Neurosci , vol.16 , pp. 299-313
    • St-Hilaire, M.1    Longtin, A.2
  • 24
    • 4644310188 scopus 로고    scopus 로고
    • Threshold firing frequency-current relationships of neurons in rat somatosensory cortex: Type 1 and Type 2 dynamics
    • Tateno, T., Harsch, A. & Robinson, H. P. C. [2004] "Threshold firing frequency-current relationships of neurons in rat somatosensory cortex: Type 1 and Type 2 dynamics," J. Neurophysiol. 92, 2283-2294.
    • (2004) J. Neurophysiol , vol.92 , pp. 2283-2294
    • Tateno, T.1    Harsch, A.2    Robinson, H.P.C.3
  • 25
    • 4344648888 scopus 로고    scopus 로고
    • Chaotic itinerancy as a mechanism of irregular changes between synchronization and desynchronization in a neural network
    • Tsuda, I., Fujii, H., Tadokoro, S., Yasuoka, T. & Yamaguti, Y. [2004] "Chaotic itinerancy as a mechanism of irregular changes between synchronization and desynchronization in a neural network," J. Integr. Neurosci. 3, 159-182.
    • (2004) J. Integr. Neurosci , vol.3 , pp. 159-182
    • Tsuda, I.1    Fujii, H.2    Tadokoro, S.3    Yasuoka, T.4    Yamaguti, Y.5
  • 27
    • 0033592662 scopus 로고    scopus 로고
    • Simplified dynamics of human and mammalian neocortical neurons
    • Wilson, H. R. [1999] "Simplified dynamics of human and mammalian neocortical neurons," J. Theor. Biol. 200, 375-388.
    • (1999) J. Theor. Biol , vol.200 , pp. 375-388
    • Wilson, H.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.