메뉴 건너뛰기




Volumn 240, Issue 1, 2011, Pages 13-20

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

Author keywords

Delay equations; Integrodifferential equations; Mathematical neuroscience; Neural field equation; Spectra

Indexed keywords

ATMOSPHERIC SPECTRA; DISPERSION (WAVES); DISPERSIONS; EIGENVALUES AND EIGENFUNCTIONS; QUANTUM THEORY;

EID: 78649331376     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2010.08.002     Document Type: Article
Times cited : (16)

References (34)
  • 3
    • 0000076718 scopus 로고
    • Observations variae in mathesin puram
    • J.H. Lambert Observations variae in mathesin puram Acta Helv. 3 1758 128 168 physico-mathematico-anatomico-botanico-medica
    • (1758) Acta Helv. , vol.3 , pp. 128-168
    • Lambert, J.H.1
  • 4
    • 0141830923 scopus 로고    scopus 로고
    • Analysis of a system of linear delay differential equations
    • F. Asl, and A.G. Ulsoy Analysis of a system of linear delay differential equations J. Dyn. Syst. Meas. Control 125 2003 215 223
    • (2003) J. Dyn. Syst. Meas. Control , vol.125 , pp. 215-223
    • Asl, F.1    Ulsoy, A.G.2
  • 6
    • 0017713690 scopus 로고
    • Dynamics of pattern formation in lateral inhibition type neural fields
    • S.I. Amari Dynamics of pattern formation in lateral inhibition type neural fields Biol. Cybernet. 27 1977 77 87
    • (1977) Biol. Cybernet. , vol.27 , pp. 77-87
    • Amari, S.I.1
  • 7
    • 70350714925 scopus 로고    scopus 로고
    • Inverse problems in neural field theory
    • P. Beim Graben, and R. Potthast Inverse problems in neural field theory SIAM J. Appl. Dyn. Syst. 8 4 2009 1405 1433
    • (2009) SIAM J. Appl. Dyn. Syst. , vol.8 , Issue.4 , pp. 1405-1433
    • Beim Graben, P.1    Potthast, R.2
  • 8
    • 0015868589 scopus 로고
    • A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue
    • H.R. Wilson, and J.D. Cowan A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue Kybernetika 13 1973 55 80
    • (1973) Kybernetika , vol.13 , pp. 55-80
    • Wilson, H.R.1    Cowan, J.D.2
  • 9
    • 0037446036 scopus 로고    scopus 로고
    • Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
    • S. Coombes, G.J. Lord, and M.R. Owen Waves and bumps in neuronal networks with axo-dendritic synaptic interactions Physica D 178 2008 219 241
    • (2008) Physica D , vol.178 , pp. 219-241
    • Coombes, S.1    Lord, G.J.2    Owen, M.R.3
  • 10
    • 34347403426 scopus 로고    scopus 로고
    • Dynamic instabilities in scalar neural field equations with space-dependent delays
    • N.A. Venkov, S. Coombes, and P.C. Matthews Dynamic instabilities in scalar neural field equations with space-dependent delays Physica D 232 2007 1 15
    • (2007) Physica D , vol.232 , pp. 1-15
    • Venkov, N.A.1    Coombes, S.2    Matthews, P.C.3
  • 11
    • 23944441267 scopus 로고    scopus 로고
    • Waves, bumps, and patterns in neural field theories
    • S. Coombes Waves, bumps, and patterns in neural field theories Biol. Cybernet. 93 2005 91 108
    • (2005) Biol. Cybernet. , vol.93 , pp. 91-108
    • Coombes, S.1
  • 12
    • 56449114765 scopus 로고    scopus 로고
    • Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections
    • W.C. Troy Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections SIAM J. Appl. Dyn. Syst. 7 2008 1247
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , pp. 1247
    • Troy, W.C.1
  • 13
    • 17544363017 scopus 로고    scopus 로고
    • Analysis of nonlocal neural fields for both general and gamma-distributed connectivities
    • A. Hutt, and F.M. Atay Analysis of nonlocal neural fields for both general and gamma-distributed connectivities Physica D 203 2005 30
    • (2005) Physica D , vol.203 , pp. 30
    • Hutt, A.1    Atay, F.M.2
  • 14
    • 17544362949 scopus 로고    scopus 로고
    • Stability and bifurcations in neural fields with finite propagation speed and general connectivity
    • F.M. Atay, and A. Hutt Stability and bifurcations in neural fields with finite propagation speed and general connectivity SIAM J. Appl. Math. 65 2 2005 644
    • (2005) SIAM J. Appl. Math. , vol.65 , Issue.2 , pp. 644
    • Atay, F.M.1    Hutt, A.2
  • 15
    • 0032570706 scopus 로고    scopus 로고
    • Propagating activity patterns in large-scale inhibitory neuronal networks
    • J. Rinzel, D. Terman, X.-J. Wang, and B. Ermentrout Propagating activity patterns in large-scale inhibitory neuronal networks Science 279 1998 1351
    • (1998) Science , vol.279 , pp. 1351
    • Rinzel, J.1    Terman, D.2    Wang, X.-J.3    Ermentrout, B.4
  • 16
    • 16244415210 scopus 로고    scopus 로고
    • Front bifurcations in an excitatory neural network
    • P. Bressloff, and S.E. Folias Front bifurcations in an excitatory neural network SIAM J. Appl. Math. 65 2004 131 151
    • (2004) SIAM J. Appl. Math. , vol.65 , pp. 131-151
    • Bressloff, P.1    Folias, S.E.2
  • 17
    • 0037135809 scopus 로고    scopus 로고
    • Bloch waves, periodic feature maps, and cortical pattern formation
    • P.C. Bressloff Bloch waves, periodic feature maps, and cortical pattern formation Phys. Rev. Lett. 89 2002
    • (2002) Phys. Rev. Lett. , vol.89
    • Bressloff, P.C.1
  • 18
    • 18144426424 scopus 로고    scopus 로고
    • Bumps, breathers, and waves in a neural network with spike frequency adaptation
    • S. Coombes, and M.R. Owen Bumps, breathers, and waves in a neural network with spike frequency adaptation Phys. Rev. Lett. 94 2005 148102
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 148102
    • Coombes, S.1    Owen, M.R.2
  • 19
    • 20444449197 scopus 로고    scopus 로고
    • Existence and stability of standing pulses in neural networks: I. Existence
    • DOI 10.1137/040609471
    • Y. Guo, and C.C. Chow Existence and stability of standing pulses in neural networks: I. Existence SIAM J. Appl. Dyn. Syst. 4 2005 217 248 (Pubitemid 43385174)
    • (2005) SIAM Journal on Applied Dynamical Systems , vol.4 , Issue.2 , pp. 217-248
    • Guo, Y.1    Chow, C.C.2
  • 20
    • 20444456171 scopus 로고    scopus 로고
    • Existence and stability of standing pulses in neural networks: II. Stability
    • DOI 10.1137/040609483
    • Y. Guo, and C.C. Chow Existence and stability of standing pulses in neural networks: II. Stability SIAM J. Appl. Dyn. Syst. 4 2005 249 281 (Pubitemid 43385175)
    • (2005) SIAM Journal on Applied Dynamical Systems , vol.4 , Issue.2 , pp. 249-281
    • Guo, Y.1    Chow, C.C.2
  • 21
    • 0037446124 scopus 로고    scopus 로고
    • Two-bump solutions of Amari type models of working memory
    • C.R. Laing, and W.C. Troy Two-bump solutions of Amari type models of working memory Physica D 178 2003 190 218
    • (2003) Physica D , vol.178 , pp. 190-218
    • Laing, C.R.1    Troy, W.C.2
  • 24
    • 0036226617 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: 1 traveling fronts and pulses
    • J.D. Pinto, and G.B. Ermentrout Spatially structured activity in synaptically coupled neuronal networks: 1 traveling fronts and pulses SIAM J. Appl. Math. 62 2002 206 225
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 206-225
    • Pinto, J.D.1    Ermentrout, G.B.2
  • 25
    • 0036229681 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: 2 lateral inhibition and standing pulses
    • J.D. Pinto, and G.B. Ermentrout Spatially structured activity in synaptically coupled neuronal networks: 2 lateral inhibition and standing pulses SIAM J. Appl. Math. 62 2002 226 243
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 226-243
    • Pinto, J.D.1    Ermentrout, G.B.2
  • 26
    • 23944491928 scopus 로고    scopus 로고
    • Existence and stability of traveling pulses in a continuous neuronal network
    • J.D. Pinto, K.R. Jackson, and C.E. Wayne Existence and stability of traveling pulses in a continuous neuronal network SIAM J. Appl. Dyn. Syst. 4 2005 954 984
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , pp. 954-984
    • Pinto, J.D.1    Jackson, K.R.2    Wayne, C.E.3
  • 27
    • 0034902811 scopus 로고    scopus 로고
    • Localized bumps of activity sustained by inhibition in a two-layer thalamic network
    • J.E. Rubin, D. Terman, and C.C. Chow Localized bumps of activity sustained by inhibition in a two-layer thalamic network J. Comput. Neurosci. 10 2001 313 331
    • (2001) J. Comput. Neurosci. , vol.10 , pp. 313-331
    • Rubin, J.E.1    Terman, D.2    Chow, C.C.3
  • 28
    • 2942531288 scopus 로고    scopus 로고
    • Sustained spatial patterns of activity in neuronal populations with or without lateral inhibition
    • J.E. Rubin, and W.C. Troy Sustained spatial patterns of activity in neuronal populations with or without lateral inhibition SIAM J. Appl. Math. 84 5 2004 1809
    • (2004) SIAM J. Appl. Math. , vol.84 , Issue.5 , pp. 1809
    • Rubin, J.E.1    Troy, W.C.2
  • 29
    • 34748836908 scopus 로고    scopus 로고
    • Evens functions and nonlinear stability of traveling waves in neuronal network models
    • B. Sandstede Evens functions and nonlinear stability of traveling waves in neuronal network models Internat. J. Bifur. Chaos 17 2007 2693 2704
    • (2007) Internat. J. Bifur. Chaos , vol.17 , pp. 2693-2704
    • Sandstede, B.1
  • 30
    • 1042287949 scopus 로고    scopus 로고
    • On stability of traveling wave solutions in synaptically coupled neuronal networks
    • L. Zhang On stability of traveling wave solutions in synaptically coupled neuronal networks Differential Integral Equations 16 2003 513 536
    • (2003) Differential Integral Equations , vol.16 , pp. 513-536
    • Zhang, L.1
  • 31
    • 35949003696 scopus 로고    scopus 로고
    • Modeling electrocortical activity through improved local approximations of integral neural field equations
    • S. Coombes, N.A. Venkov, L. Shiau, I. Bojak, D.T.J. Liley, and C.R. Laing Modeling electrocortical activity through improved local approximations of integral neural field equations Phys. Rev. E 76 2007 051901-8
    • (2007) Phys. Rev. e , vol.76 , pp. 051901-051908
    • Coombes, S.1    Venkov, N.A.2    Shiau, L.3    Bojak, I.4    Liley, D.T.J.5    Laing, C.R.6
  • 32
    • 0030786828 scopus 로고    scopus 로고
    • A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics
    • V.K. Jirsa, and H. Haken A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics Physica D 99 1997 503 526
    • (1997) Physica D , vol.99 , pp. 503-526
    • Jirsa, V.K.1    Haken, H.2
  • 33
    • 33749542056 scopus 로고    scopus 로고
    • Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay
    • A. Hutt, and F.M. Atay Spontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay Chaos Solitons Fractals 32 2007 547
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 547
    • Hutt, A.1    Atay, F.M.2
  • 34
    • 52049094543 scopus 로고    scopus 로고
    • The role of fMRI in cognitive neuroscience: Where do we stand?
    • R.A. Poldrack The role of fMRI in cognitive neuroscience: where do we stand? Curr. Opin. Neurobiol. 18 2008 223 227
    • (2008) Curr. Opin. Neurobiol. , vol.18 , pp. 223-227
    • Poldrack, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.