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Volumn 16, Issue 4, 2009, Pages 535-549

Asymptotic dynamics of the slow-fast hindmarsh-rose neuronal system

Author keywords

Asymptotic dynamics; Bifurcation; Chaos; Neuron model

Indexed keywords


EID: 70449723652     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (19)

References (14)
  • 1
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    • Synchronization of bursting neurons: What matters in the network topology
    • I. Belykh, E. Lange, M. Hasler , Synchronization of Bursting Neurons: What matters in the Network Topology, Phy. Rev. Lett.94, 18, (2005) 188101.1-188101.4.
    • (2005) Phy. Rev. Lett. , vol.94 , Issue.18 , pp. 1881011-1881014
    • Belykh, I.1    Lange, E.2    Hasler, M.3
  • 5
    • 36749092272 scopus 로고    scopus 로고
    • Complex bifurcation structures in the Hindmarsh-Rose neuron model
    • J.M. Gonzalez-Miranda, Complex bifurcation structures in the Hindmarsh-Rose neuron model, Int. J. of Bifurcation and Chaos 17, 9, (2007) 3071-3083.
    • (2007) Int. J. of Bifurcation and Chaos , vol.17 , Issue.9 , pp. 3071-3083
    • Gonzalez-Miranda, J.M.1
  • 6
    • 77955400172 scopus 로고    scopus 로고
    • Bifurcations in the fast dynamics of neurons: Implications for bursting, Bursting, the Genesis of Rhythm in the Nervous System
    • Stephen Coombes and Paul C Bressloff
    • J. Guckenheimer, J. Tien and A. Willms, Bifurcations in the fast dynamics of neurons: implications for bursting, Bursting, The Genesis of Rhythm in the Nervous System, Eds. Stephen Coombes and Paul C Bressloff, World Scientific, 2005, pp. 89-122.
    • (2005) World Scientific , pp. 89-122
    • Guckenheimer, J.1    Tien, J.2    Willms, A.3
  • 8
    • 0020049721 scopus 로고
    • A model of the nerve impulse using two first-order differential equations
    • J.L. Hindmarsh, R.M. Rose, A model of the nerve impulse using two first-order differential equations, Nature 296, (1982), 162-164.
    • (1982) Nature , vol.296 , pp. 162-164
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 9
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first order differential equations
    • J.L. Hindmarsh, R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Sc. Lond. B221, (1984) 87-102.
    • (1984) Proc. R. Sc. Lond. , vol.B221 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 10
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • A. Hodgkin, A. Huxley, A quantitative description of membrane current 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.1    Huxley, A.2
  • 11
    • 37649016614 scopus 로고    scopus 로고
    • Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos
    • 043128
    • G. Innocenti, A. Morelli, R. Genesio, A. Torcini, Dynamical phases of the Hindmarsh-Rose neuronal model : Studies of the transition from bursting to spiking chaos, Chaos 17, 043128, (2007) 1-11.
    • (2007) Chaos , vol.17 , pp. 1-11
    • Innocenti, G.1    Morelli, A.2    Genesio, R.3    Torcini, A.4
  • 13
    • 54949130175 scopus 로고    scopus 로고
    • Methods of the qualitative theory for the HindmarshRose model: A case study
    • A.L. Shilnikov, M.L. Kolomiets, Methods of the qualitative theory for the HindmarshRose model : a case study, Tutorial. J. Bifurcations and Chaos 18, 8, (2007) 1-27.
    • (2007) Tutorial. J. Bifurcations and Chaos , vol.18 , Issue.8 , pp. 1-27
    • Shilnikov, A.L.1    Kolomiets, M.L.2
  • 14
    • 70449708153 scopus 로고    scopus 로고
    • Periodic orbits of tritrophic slow-fast system and double homoclinic bifurcations
    • special volume
    • A. Vidal, Periodic orbits of tritrophic slow-fast system and double homoclinic bifurcations, Discrete and Continuous Dynamical Systems - Series B, special volume, (2007) 1021-1030.
    • (2007) Discrete and Continuous Dynamical Systems - Series B , pp. 1021-1030
    • Vidal, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.