메뉴 건너뛰기




Volumn 239, Issue 9, 2010, Pages 504-514

Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network

Author keywords

Canards; Double homoclinics; Mixed mode oscillations; Neural systems; Period doubling and Neimark Sacker bifurcations; Singular Hopf

Indexed keywords

BINOCULAR VISION; CHAOS THEORY; FEEDBACK; NEURAL NETWORKS;

EID: 77349110426     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2009.12.010     Document Type: Article
Times cited : (95)

References (38)
  • 1
    • 36749113474 scopus 로고
    • An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinskii reaction
    • Hudson J., Hart M., and Marinko D. An experimental study of multiple peak periodic and nonperiodic oscillations in the Belousov-Zhabotinskii reaction. J. Chem. Phys. 71 (1979) 1601-1606
    • (1979) J. Chem. Phys. , vol.71 , pp. 1601-1606
    • Hudson, J.1    Hart, M.2    Marinko, D.3
  • 2
    • 0009197412 scopus 로고
    • Mixed-mode oscillations in chemical systems
    • Petrov V., Scott S.K., and Showalter K. Mixed-mode oscillations in chemical systems. J. Chem. Phys. 97 9 (1992) 6191-6198
    • (1992) J. Chem. Phys. , vol.97 , Issue.9 , pp. 6191-6198
    • Petrov, V.1    Scott, S.K.2    Showalter, K.3
  • 3
    • 0000089576 scopus 로고
    • A hierarchy of transitions to mixed mode oscillations in an electrochemical system
    • Krischer K., Lübke M., Eiswirth M., Wolf W., Hudson J.L., and Ertl G. A hierarchy of transitions to mixed mode oscillations in an electrochemical system. Physica D 62 (1993) 123-133
    • (1993) Physica D , vol.62 , pp. 123-133
    • Krischer, K.1    Lübke, M.2    Eiswirth, M.3    Wolf, W.4    Hudson, J.L.5    Ertl, G.6
  • 4
    • 0030219251 scopus 로고    scopus 로고
    • Nonlinear chemical dynamics: Oscillations, patterns, and chaos
    • Epstein I.R., and Showalter K. Nonlinear chemical dynamics: Oscillations, patterns, and chaos. J. Phys. Chem. 100 (1996) 13132-13147
    • (1996) J. Phys. Chem. , vol.100 , pp. 13132-13147
    • Epstein, I.R.1    Showalter, K.2
  • 5
    • 0034721176 scopus 로고    scopus 로고
    • Oscillatory cluster patterns in a homogeneous chemical system with global feedback
    • Vanag V.K., Yang L., Dolnik M., Zhabotinsky A.M., and Epstein I.R. Oscillatory cluster patterns in a homogeneous chemical system with global feedback. Nature 406 (2000) 389-391
    • (2000) Nature , vol.406 , pp. 389-391
    • Vanag, V.K.1    Yang, L.2    Dolnik, M.3    Zhabotinsky, A.M.4    Epstein, I.R.5
  • 6
    • 0037984245 scopus 로고    scopus 로고
    • Pattern formation in the Belousov-Zhabotinsky reaction with photochemical global feedback
    • Vanag V.K., Zhabotinsky A.M., and Epstein I.R. Pattern formation in the Belousov-Zhabotinsky reaction with photochemical global feedback. J. Phys. Chem. A 104 (2000) 11566-11577
    • (2000) J. Phys. Chem. A , vol.104 , pp. 11566-11577
    • Vanag, V.K.1    Zhabotinsky, A.M.2    Epstein, I.R.3
  • 7
    • 60549108829 scopus 로고    scopus 로고
    • Small-amplitude and mixed-mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system
    • Kovacs K., Leda M., Vanag V.K., and Epstein I.R. Small-amplitude and mixed-mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system. J. Phys. Chem. A 113 (2009) 146-156
    • (2009) J. Phys. Chem. A , vol.113 , pp. 146-156
    • Kovacs, K.1    Leda, M.2    Vanag, V.K.3    Epstein, I.R.4
  • 8
    • 0003737187 scopus 로고    scopus 로고
    • Mixed-mode oscillations and chaos in a glow discharge
    • Hayashi T. Mixed-mode oscillations and chaos in a glow discharge. Phys. Rev. Lett. 84 (2000) 3334-3337
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 3334-3337
    • Hayashi, T.1
  • 10
    • 0024965794 scopus 로고
    • +-dependent theta like rhythmicity in stellate cells of entorhinal cortex layer II
    • +-dependent theta like rhythmicity in stellate cells of entorhinal cortex layer II. Nature 342 (1989) 175-177
    • (1989) Nature , vol.342 , pp. 175-177
    • Alonso, A.A.1    Llinás, R.R.2
  • 11
    • 0036219109 scopus 로고    scopus 로고
    • Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network
    • Del Negro C.A., Wilson C.G., Butera R.J., Rigatto H., and Smith J.C. Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network. Biophys. J. 82 (2002) 206-214
    • (2002) Biophys. J. , vol.82 , pp. 206-214
    • Del Negro, C.A.1    Wilson, C.G.2    Butera, R.J.3    Rigatto, H.4    Smith, J.C.5
  • 12
    • 2942560675 scopus 로고    scopus 로고
    • Multimodal regimes in a compartmental model of the dopamine neuron
    • Medvedev G., and Cisternas J.E. Multimodal regimes in a compartmental model of the dopamine neuron. Physica D 194 3-4 (2004) 333-356
    • (2004) Physica D , vol.194 , Issue.3-4 , pp. 333-356
    • Medvedev, G.1    Cisternas, J.E.2
  • 13
    • 33644860455 scopus 로고    scopus 로고
    • Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron
    • Kuznetsov A., Kopell N., and Wilson C. Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron. J. Neurophysiol. 95 (2006) 932-947
    • (2006) J. Neurophysiol. , vol.95 , pp. 932-947
    • Kuznetsov, A.1    Kopell, N.2    Wilson, C.3
  • 14
    • 41549101374 scopus 로고    scopus 로고
    • The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales
    • 015105
    • Rubin J., and Wechselberger M. The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos 18 (2008) 1-12 015105
    • (2008) Chaos , vol.18 , pp. 1-12
    • Rubin, J.1    Wechselberger, M.2
  • 15
    • 63049107517 scopus 로고    scopus 로고
    • Canards, clusters and synchronization in a weakly coupled interneuron model
    • Ermentrout B., and Wechselberger M. Canards, clusters and synchronization in a weakly coupled interneuron model. SIAM J. Appl. Dyn. Syst. 8 1 (2009) 253-278
    • (2009) SIAM J. Appl. Dyn. Syst. , vol.8 , Issue.1 , pp. 253-278
    • Ermentrout, B.1    Wechselberger, M.2
  • 16
    • 63049099934 scopus 로고    scopus 로고
    • Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model
    • Rotstein H., Wechselberger M., and Kopell N. Canard induced mixed-mode oscillations in a medial entorhinal cortex layer II stellate cell model. SIAM J. Appl. Dyn. Syst. 7 (2008) 1582-1611
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 1582-1611
    • Rotstein, H.1    Wechselberger, M.2    Kopell, N.3
  • 17
  • 18
    • 0002467474 scopus 로고
    • Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram
    • Koper M.T.M. Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram. Physica D 80 (1995) 72-94
    • (1995) Physica D , vol.80 , pp. 72-94
    • Koper, M.T.M.1
  • 20
    • 0346687131 scopus 로고    scopus 로고
    • Asymptotic analysis of subcritical Hopf-homoclinic bifurcation
    • Guckenheimer J., and Willms A. Asymptotic analysis of subcritical Hopf-homoclinic bifurcation. Physica D 139 (2000) 195-216
    • (2000) Physica D , vol.139 , pp. 195-216
    • Guckenheimer, J.1    Willms, A.2
  • 22
    • 34547347930 scopus 로고    scopus 로고
    • Mixed mode oscillations due to the generalized canard phenomenon
    • Brons M., Krupa M., and Wechselberger M. Mixed mode oscillations due to the generalized canard phenomenon. Fields Inst. Commun. 49 (2006) 39-63
    • (2006) Fields Inst. Commun. , vol.49 , pp. 39-63
    • Brons, M.1    Krupa, M.2    Wechselberger, M.3
  • 23
    • 0344467289 scopus 로고    scopus 로고
    • Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback
    • Rotstein H., Kopell N., Zhabotinsky A.M., and Epstein I.R. Canard phenomenon and localization of oscillations in the Belousov-Zhabotinsky reaction with global feedback. J. Chem. Phys. 119 (2003) 8824-8832
    • (2003) J. Chem. Phys. , vol.119 , pp. 8824-8832
    • Rotstein, H.1    Kopell, N.2    Zhabotinsky, A.M.3    Epstein, I.R.4
  • 24
    • 16244415882 scopus 로고    scopus 로고
    • Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies
    • Drover J., Rubin J., Su J., and Ermentrout B. Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies. SIAM J. Appl. Math. 62 1 (2004) 69-92
    • (2004) SIAM J. Appl. Math. , vol.62 , Issue.1 , pp. 69-92
    • Drover, J.1    Rubin, J.2    Su, J.3    Ermentrout, B.4
  • 25
    • 56449117107 scopus 로고    scopus 로고
    • Singular Hopf bifurcation in systems with two slow variables
    • Guckenheimer J. Singular Hopf bifurcation in systems with two slow variables. SIAM J. Appl. Dyn. Syst. 7 4 (2008) 1355-1377
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , Issue.4 , pp. 1355-1377
    • Guckenheimer, J.1
  • 29
    • 0036256356 scopus 로고    scopus 로고
    • A spiking neuron model for binocular rivalry
    • Laing C.R., and Chow C.C. A spiking neuron model for binocular rivalry. J. Comput. Neurosci. 12 (2002) 39-53
    • (2002) J. Comput. Neurosci. , vol.12 , pp. 39-53
    • Laing, C.R.1    Chow, C.C.2
  • 30
    • 57249086523 scopus 로고    scopus 로고
    • Mechanisms for frequency control in neuronal competition models
    • Curtu R., Shpiro A., Rubin N., and Rinzel J. Mechanisms for frequency control in neuronal competition models. SIAM J. Appl. Dyn. Syst. 7 2 (2008) 609-649
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , Issue.2 , pp. 609-649
    • Curtu, R.1    Shpiro, A.2    Rubin, N.3    Rinzel, J.4
  • 31
    • 33846455499 scopus 로고    scopus 로고
    • Dynamical characteristics common to neuronal competition models
    • Shpiro A., Curtu R., Rinzel J., and Rubin N. Dynamical characteristics common to neuronal competition models. J. Neurophysiol. 97 (2007) 462-473
    • (2007) J. Neurophysiol. , vol.97 , pp. 462-473
    • Shpiro, A.1    Curtu, R.2    Rinzel, J.3    Rubin, N.4
  • 32
    • 0002585608 scopus 로고
    • Half-center oscillators underlying rhythmic movements
    • Arbib M.A. (Ed), MIT Press, Cambridge, MA
    • Calabrese R.L. Half-center oscillators underlying rhythmic movements. In: Arbib M.A. (Ed). The Handbook of Brain Theory and Neural Networks (1995), MIT Press, Cambridge, MA 444-447
    • (1995) The Handbook of Brain Theory and Neural Networks , pp. 444-447
    • Calabrese, R.L.1
  • 33
    • 0028457504 scopus 로고
    • Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks
    • Skinner F.K., Kopell N., and Marder E. Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J. Comput. Neurosci. 1 (1994) 69-87
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 69-87
    • Skinner, F.K.1    Kopell, N.2    Marder, E.3
  • 34
    • 0036514268 scopus 로고    scopus 로고
    • Analysis of oscillations in a reciprocally inhibitory network with synaptic depression
    • Taylor A.L., Cottrell G.W., and Kristan W.B. Analysis of oscillations in a reciprocally inhibitory network with synaptic depression. Neural Comput. 14 (2002) 561-581
    • (2002) Neural Comput. , vol.14 , pp. 561-581
    • Taylor, A.L.1    Cottrell, G.W.2    Kristan, W.B.3
  • 35
    • 0011924251 scopus 로고    scopus 로고
    • Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students
    • SIAM, Philadelphia
    • Ermentrout B. Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. Software Environ. Tools vol. 14 (2002), SIAM, Philadelphia
    • (2002) Software Environ. Tools , vol.14
    • Ermentrout, B.1
  • 36
    • 77349116702 scopus 로고    scopus 로고
    • Ermentrout B. http://www.math.pitt.edu/~bard/xpp/xpp.html
    • Ermentrout, B.1
  • 37
    • 8744230577 scopus 로고    scopus 로고
    • MATCONT: A Matlab package for numerical bifurcation analysis of ODEs
    • Dhooge A., Govaerts W., and Kuznetsov Yu.A. MATCONT: A Matlab package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Software 29 (2003) 141-164. http://www.matcont.ugent.be/
    • (2003) ACM Trans. Math. Software , vol.29 , pp. 141-164
    • Dhooge, A.1    Govaerts, W.2    Kuznetsov, Yu.A.3
  • 38
    • 0042865283 scopus 로고    scopus 로고
    • Singular Hopf bifurcation in systems with fast and slow variables
    • Braaksma B. Singular Hopf bifurcation in systems with fast and slow variables. J. Nonlinear Sci. 8 (1998) 457-490
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 457-490
    • Braaksma, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.