메뉴 건너뛰기




Volumn 71, Issue 4, 2006, Pages 544-564

Wave-front solution behaviour for continuous neural networks with lateral inhibition

Author keywords

Integral differential equations; Neural fields; Travelling wave solutions; Wave front shape

Indexed keywords

CELLS; ENZYME INHIBITION; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS;

EID: 33748055128     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxl007     Document Type: Article
Times cited : (4)

References (63)
  • 1
    • 0017713690 scopus 로고
    • Dynamics of pattern formation in lateral-inhibition type neural fields
    • Amari, S. I. (1977) Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern., 27, 77-87.
    • (1977) Biol. Cybern. , vol.27 , pp. 77-87
    • Amari, S.I.1
  • 3
    • 17544362949 scopus 로고    scopus 로고
    • Stability and bifurcations in neural fields with finite propagation speed and general connectivity
    • Atay, F. M. & Hutt, A. (2004) Stability and bifurcations in neural fields with finite propagation speed and general connectivity. SIAM J. Appl. Math., 65, 644-666.
    • (2004) SIAM J. Appl. Math. , vol.65 , pp. 644-666
    • Atay, F.M.1    Hutt, A.2
  • 4
    • 0031282920 scopus 로고    scopus 로고
    • Traveling waves in a convolution model for phase transitions
    • Bates, P. W., Fife, P. C., Ren, X. & Wang, X. (1997) Traveling waves in a convolution model for phase transitions. Arch. Ration. Mech. Anal., 138, 105-136.
    • (1997) Arch. Ration. Mech. Anal. , vol.138 , pp. 105-136
    • Bates, P.W.1    Fife, P.C.2    Ren, X.3    Wang, X.4
  • 6
    • 0022545418 scopus 로고
    • Voltage-sensitive dyes reveal a modular organization in monkey striate cortex
    • Blasdel, G. G. & Salama, G. (1986) Voltage-sensitive dyes reveal a modular organization in monkey striate cortex. Nature, 321, 579-585.
    • (1986) Nature , vol.321 , pp. 579-585
    • Blasdel, G.G.1    Salama, G.2
  • 7
    • 0001677215 scopus 로고    scopus 로고
    • New mechanism for neural pattern formation
    • Bressloff, P. C. (1996) New mechanism for neural pattern formation. Phys. Rev. Lett., 76, 4644-4647.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 4644-4647
    • Bressloff, P.C.1
  • 8
    • 0001068180 scopus 로고    scopus 로고
    • Synchrony in an array of integrate-and-fire neurons with dendritic structure
    • Bressloff, P. C. & Coombes, S. (1997) Synchrony in an array of integrate-and-fire neurons with dendritic structure. Phys. Rev. Lett., 78, 4665-4668.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 4665-4668
    • Bressloff, P.C.1    Coombes, S.2
  • 11
    • 33748069711 scopus 로고    scopus 로고
    • Uniform stability of multidimensional travelling waves for the nonlocal Allen-Cahn equation
    • Chen, F. (2003) Uniform stability of multidimensional travelling waves for the nonlocal Allen-Cahn equation. Electron J. Differ. Equ. Conf., 10, 109-113.
    • (2003) Electron J. Differ. Equ. Conf. , vol.10 , pp. 109-113
    • Chen, F.1
  • 12
    • 0023734648 scopus 로고
    • Periodicity and directionality in the propagation of epileptiform discharges across neocortex
    • Chervin, R. D., Pierce, P. A. & Connors, B. W. (1988) Periodicity and directionality in the propagation of epileptiform discharges across neocortex. J. Neurophysiol., 60, 1695-1713.
    • (1988) J. Neurophysiol. , vol.60 , pp. 1695-1713
    • Chervin, R.D.1    Pierce, P.A.2    Connors, B.W.3
  • 13
    • 0028971729 scopus 로고
    • Oculocentric spatial representation in parietal cortex
    • Colby, C. L., Duhamel, J. R. & Goldberg, M. E. (1995) Oculocentric spatial representation in parietal cortex. Cereb. Cortex, 5, 470-481.
    • (1995) Cereb. Cortex , vol.5 , pp. 470-481
    • Colby, C.L.1    Duhamel, J.R.2    Goldberg, M.E.3
  • 14
    • 0002469245 scopus 로고
    • Generation of epileptiform discharge by local circuits in neocortex
    • (P. A. Schwartzkroin ed). Cambridge: Cambridge University Press
    • Connors, B. W. & Amitai, Y. (1993) Generation of epileptiform discharge by local circuits in neocortex. Epilepsy: Models, Mechanisms and Concepts (P. A. Schwartzkroin ed). Cambridge: Cambridge University Press, pp. 388-423.
    • (1993) Epilepsy: Models, Mechanisms and Concepts , pp. 388-423
    • Connors, B.W.1    Amitai, Y.2
  • 15
    • 0037446036 scopus 로고    scopus 로고
    • Waves and bumps in neuronal networks with axo-dendritic synaptic interactions
    • Coombes, S., Lord, G. J. & Owen, M. R. (2003) Waves and bumps in neuronal networks with axo-dendritic synaptic interactions. Physica D, 178, 219-241.
    • (2003) Physica D , vol.178 , pp. 219-241
    • Coombes, S.1    Lord, G.J.2    Owen, M.R.3
  • 16
    • 4344605081 scopus 로고    scopus 로고
    • A note on traveling fronts and pulses in a firing rate model of a neuronal network
    • Enculescu, M. (2004) A note on traveling fronts and pulses in a firing rate model of a neuronal network. Physica D, 196, 362-386.
    • (2004) Physica D , vol.196 , pp. 362-386
    • Enculescu, M.1
  • 17
    • 0001104658 scopus 로고    scopus 로고
    • Neural networks as spatio-temporal pattern-forming systems
    • Ermentrout, B. (1998) Neural networks as spatio-temporal pattern-forming systems. Rep. Prog. Phys., 61, 353-430.
    • (1998) Rep. Prog. Phys. , vol.61 , pp. 353-430
    • Ermentrout, B.1
  • 18
    • 7044258434 scopus 로고
    • A model for premigrainous auras
    • (A. H. Holden & W. Winlow eds). Manchester: Manchester University Press
    • Ermentrout, G. B. (1984) A model for premigrainous auras. The Neurobiology of Pain (A. H. Holden & W. Winlow eds). Manchester: Manchester University Press, pp. 267-283.
    • (1984) The Neurobiology of Pain , pp. 267-283
    • Ermentrout, G.B.1
  • 19
    • 0018700147 scopus 로고
    • A mathematical theory of visual hallucination patterns
    • Ermentrout, G. B. & Cowan, J. D. (1979) A mathematical theory of visual hallucination patterns. Biol. Cybern., 34, 137-150.
    • (1979) Biol. Cybern. , vol.34 , pp. 137-150
    • Ermentrout, G.B.1    Cowan, J.D.2
  • 20
    • 84971116294 scopus 로고
    • Existence and uniqueness of travelling waves for a neural network
    • Ermentrout, G. B. & McLeod, J. B. (1993) Existence and uniqueness of travelling waves for a neural network. Proc. R. Soc. Edinb. Sect. A, 123, 461-478.
    • (1993) Proc. R. Soc. Edinb. Sect. A , vol.123 , pp. 461-478
    • Ermentrout, G.B.1    McLeod, J.B.2
  • 21
    • 16344393249 scopus 로고    scopus 로고
    • Breathing pulses in an excitatory neural network
    • Folias, S. E. & Bressloff, P. C. (2004) Breathing pulses in an excitatory neural network. SIAM J. Appl. Dyn. Syst., 3, 378-407.
    • (2004) SIAM J. Appl. Dyn. Syst. , vol.3 , pp. 378-407
    • Folias, S.E.1    Bressloff, P.C.2
  • 23
    • 0028938076 scopus 로고
    • Cellular basis of working memory
    • Goldman-Rakic, P. S. (1995) Cellular basis of working memory. Neuron, 14, 477-485.
    • (1995) Neuron , vol.14 , pp. 477-485
    • Goldman-Rakic, P.S.1
  • 24
    • 0030874847 scopus 로고    scopus 로고
    • Propagating neuronal discharges in neocortical slices: Computational and experimental study
    • Golomb, D. & Amitai, Y. (1997) Propagating neuronal discharges in neocortical slices: Computational and experimental study. J. Neurophysiol., 78, 1199-1211.
    • (1997) J. Neurophysiol. , vol.78 , pp. 1199-1211
    • Golomb, D.1    Amitai, Y.2
  • 25
    • 0033539518 scopus 로고    scopus 로고
    • Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity
    • Golomb, D. & Ermentrout, G. B. (1999) Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity. Proc. Natl Acad. Sci. USA, 96, 13480-13485.
    • (1999) Proc. Natl Acad. Sci. USA , vol.96 , pp. 13480-13485
    • Golomb, D.1    Ermentrout, G.B.2
  • 26
    • 0028457501 scopus 로고
    • Synchronous oscillations in neuronal systems: Mechanisms and functions
    • Gray, C. M. (1994) Synchronous oscillations in neuronal systems: mechanisms and functions. J. Comput. Neurosci., 1, 11-38.
    • (1994) J. Comput. Neurosci. , vol.1 , pp. 11-38
    • Gray, C.M.1
  • 27
    • 20444449197 scopus 로고    scopus 로고
    • Existence and stability of standing pulses in neural networks: I. Existence
    • Guo, Y. & Chow, C. C. (2005) Existence and stability of standing pulses in neural networks: I. Existence. SIAM J. Appl. Dyn. Syst., 4, 217-248.
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , pp. 217-248
    • Guo, Y.1    Chow, C.C.2
  • 28
    • 0026658279 scopus 로고
    • Optical imaging of epileptiform and functional activity in human cerebral cortex
    • Haglund, M. M., Ojemann, G. A. & Hochman, D. W. (1992) Optical imaging of epileptiform and functional activity in human cerebral cortex. Nature, 358, 668-671.
    • (1992) Nature , vol.358 , pp. 668-671
    • Haglund, M.M.1    Ojemann, G.A.2    Hochman, D.W.3
  • 29
    • 1642346053 scopus 로고    scopus 로고
    • On the formation of persistent states in neuronal network models of feature selectivity
    • Haskell, E. C. & Bressloff, P. C. (2003) On the formation of persistent states in neuronal network models of feature selectivity. J. Integr. Neurosci., 2, 103-123.
    • (2003) J. Integr. Neurosci. , vol.2 , pp. 103-123
    • Haskell, E.C.1    Bressloff, P.C.2
  • 31
    • 1842842203 scopus 로고    scopus 로고
    • Slow waves in mutually inhibitory neuronal networks
    • Jalics, J. (2004) Slow waves in mutually inhibitory neuronal networks. Physica D, 192, 95-122.
    • (2004) Physica D , vol.192 , pp. 95-122
    • Jalics, J.1
  • 32
    • 0029076314 scopus 로고
    • Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro
    • Kim, U., Bal, T. & McCormick, D. A. (1995) Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro. J. Neurophysiol., 74, 1301-1323.
    • (1995) J. Neurophysiol. , vol.74 , pp. 1301-1323
    • Kim, U.1    Bal, T.2    McCormick, D.A.3
  • 33
    • 0037446124 scopus 로고    scopus 로고
    • Two-bump solutions of Amari-type models of neuronal pattern formation
    • Laing, C. R. & Troy, W. C. (2003) Two-bump solutions of Amari-type models of neuronal pattern formation. Physica D, 178, 190-218.
    • (2003) Physica D , vol.178 , pp. 190-218
    • Laing, C.R.1    Troy, W.C.2
  • 35
    • 0027617821 scopus 로고
    • Current concepts of migraine pathogenesis
    • Lance, J. W. (1993) Current concepts of migraine pathogenesis. Neurology, 43, S11-S15.
    • (1993) Neurology , vol.43
    • Lance, J.W.1
  • 36
    • 0023757093 scopus 로고
    • Spread of synchronous firing in longitudinal slices from the CA3 region of hippocampus
    • Miles, R., Traub, R. D. & Wong, R. K. (1988) Spread of synchronous firing in longitudinal slices from the CA3 region of hippocampus. J. Neurophysiol., 60, 1481-1496.
    • (1988) J. Neurophysiol. , vol.60 , pp. 1481-1496
    • Miles, R.1    Traub, R.D.2    Wong, R.K.3
  • 37
    • 0029783329 scopus 로고    scopus 로고
    • Neural mechanisms of visual working memory in prefrontal cortex of the macaque
    • Miller, E. K., Erickson, C. A. & Desimore, R. (1996) Neural mechanisms of visual working memory in prefrontal cortex of the macaque. J. Neurosci., 16, 5154-5167.
    • (1996) J. Neurosci. , vol.16 , pp. 5154-5167
    • Miller, E.K.1    Erickson, C.A.2    Desimore, R.3
  • 38
    • 0000521718 scopus 로고
    • The behavior of extracellular ions during spreading depression
    • (T. Zeuthen ed.). Amsterdam: Elsevier Press
    • Nicholson, G. & Kraig, R. P. (1981) The behavior of extracellular ions during spreading depression. The Application of Ion-Selective Microelectrodes (T. Zeuthen ed.). Amsterdam: Elsevier Press, pp. 217-238.
    • (1981) The Application of Ion-Selective Microelectrodes , pp. 217-238
    • Nicholson, G.1    Kraig, R.P.2
  • 41
    • 0036226617 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: I traveling fronts and pulses
    • Pinto, D. J. & Ermentrout, G. B. (2001a) Spatially structured activity in synaptically coupled neuronal networks: I traveling fronts and pulses. SIAM J. Appl. Math., 62, 206-225.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 206-225
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 42
    • 0036229681 scopus 로고    scopus 로고
    • Spatially structured activity in synaptically coupled neuronal networks: II lateral inhibition and standing pulses
    • Pinto, D. J. & Ermentrout, G. B. (2001b) Spatially structured activity in synaptically coupled neuronal networks: II lateral inhibition and standing pulses. SIAM J. Appl. Math., 62, 226-243.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 226-243
    • Pinto, D.J.1    Ermentrout, G.B.2
  • 44
  • 45
    • 2942531288 scopus 로고    scopus 로고
    • Sustained spatial patterns of activity in neuronal populations without recurrent excitation
    • Rubin, J. E. & Troy, W. C. (2004) Sustained spatial patterns of activity in neuronal populations without recurrent excitation. SIAM J. Appl. Math., 64, 1609-1635.
    • (2004) SIAM J. Appl. Math. , vol.64 , pp. 1609-1635
    • Rubin, J.E.1    Troy, W.C.2
  • 46
    • 0023933891 scopus 로고
    • Dynamic pattern generation in behavioral and neural systems
    • Schöner, G. & Kelso, J. A. S. (1988) Dynamic pattern generation in behavioral and neural systems. Science, 239, 1513-1520.
    • (1988) Science , vol.239 , pp. 1513-1520
    • Schöner, G.1    Kelso, J.A.S.2
  • 47
    • 0027078465 scopus 로고
    • Temperature topography of the brain cortex: Thermoencephaloscopy
    • Shevelev, I. A. (1992) Temperature topography of the brain cortex: thermoencephaloscopy. Brain Topogr., 6, 77-85.
    • (1992) Brain Topogr. , vol.6 , pp. 77-85
    • Shevelev, I.A.1
  • 48
    • 0027481223 scopus 로고
    • Synchronization of cortical activity and its putative role in information processing and learning
    • Singer, W. (1993) Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol., 55, 349-374.
    • (1993) Annu. Rev. Physiol. , vol.55 , pp. 349-374
    • Singer, W.1
  • 49
    • 0028969330 scopus 로고
    • Visual feature integration and the temporal correlation hypothesis
    • Singer, W. & Gray, C. M. (1995) Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci., 18, 555-586.
    • (1995) Annu. Rev. Neurosci. , vol.18 , pp. 555-586
    • Singer, W.1    Gray, C.M.2
  • 50
    • 0037061682 scopus 로고    scopus 로고
    • Spatio-temporal dynamics of odor representations in the mammalian olfactory bulb
    • Spors, H. & Grindvald, A. (2002) Spatio-temporal dynamics of odor representations in the mammalian olfactory bulb. Neuron, 34, 301-315.
    • (2002) Neuron , vol.34 , pp. 301-315
    • Spors, H.1    Grindvald, A.2
  • 52
    • 0009521938 scopus 로고    scopus 로고
    • Self-organizing continuous attractor networks and path integration: One-dimensional models of head direction cells
    • Stringer, S. M., Trappenberg, T. P., Rolls, E. T. & DeAraujo, I. E. T. (2002) Self-organizing continuous attractor networks and path integration: One-dimensional models of head direction cells. Netw. Comput. Neural Syst., 13, 217-242.
    • (2002) Netw. Comput. Neural Syst. , vol.13 , pp. 217-242
    • Stringer, S.M.1    Trappenberg, T.P.2    Rolls, E.T.3    De Araujo, I.E.T.4
  • 53
    • 0018622771 scopus 로고
    • Formation of topographic maps and columnar microstructures in nerve fields
    • Takeuchi, A. & Amari, S. (1979) Formation of topographic maps and columnar microstructures in nerve fields. Biol. Cybern., 35, 63-72.
    • (1979) Biol. Cybern. , vol.35 , pp. 63-72
    • Takeuchi, A.1    Amari, S.2
  • 54
    • 0003027876 scopus 로고    scopus 로고
    • Oscillatory cortical activity during visual hallucinations
    • Tass, P. (1997) Oscillatory cortical activity during visual hallucinations. J. Biol. Phys., 23, 21-66.
    • (1997) J. Biol. Phys. , vol.23 , pp. 21-66
    • Tass, P.1
  • 55
    • 0000649277 scopus 로고    scopus 로고
    • Neural bubble dynamics in two dimensions: Foundations
    • Taylor, J. G. (1999) Neural bubble dynamics in two dimensions: foundations. Biol. Cybern., 80, 393-409.
    • (1999) Biol. Cybern. , vol.80 , pp. 393-409
    • Taylor, J.G.1
  • 56
    • 0035178331 scopus 로고    scopus 로고
    • Propagating activity patterns in thalamic neuronal networks
    • Terman, D. H., Ermentrout, G. B. & Yew, A. C. (2001) Propagating activity patterns in thalamic neuronal networks. SIAM J. Appl. Math., 61, 1578-1604.
    • (2001) SIAM J. Appl. Math. , vol.61 , pp. 1578-1604
    • Terman, D.H.1    Ermentrout, G.B.2    Yew, A.C.3
  • 57
    • 0034910549 scopus 로고    scopus 로고
    • The dynamics of embodiment: A field theory of infant perseverative reaching
    • Thelen, E., Schoner, G., Scheier, C. & Smith, L. B. (2001) The dynamics of embodiment: A field theory of infant perseverative reaching. Behav. Brain Sci., 24, 1-86.
    • (2001) Behav. Brain Sci. , vol.24 , pp. 1-86
    • Thelen, E.1    Schoner, G.2    Scheier, C.3    Smith, L.B.4
  • 58
    • 0018186904 scopus 로고
    • A mathematical model for spreading cortical depression
    • Tuckwell, H. C. & Miura, R. M. (1978) A mathematical model for spreading cortical depression. Biophys. J., 23, 257-276.
    • (1978) Biophys. J. , vol.23 , pp. 257-276
    • Tuckwell, H.C.1    Miura, R.M.2
  • 59
    • 0035458994 scopus 로고    scopus 로고
    • Circular stationary solutions in two-dimensional neural fields
    • Werner, H. & Richter, T. (2001) Circular stationary solutions in two-dimensional neural fields. Biol. Cybern., 85, 211-217.
    • (2001) Biol. Cybern. , vol.85 , pp. 211-217
    • Werner, H.1    Richter, T.2
  • 60
    • 0033564772 scopus 로고    scopus 로고
    • Propagating activation during oscillations and evoked responses in neocortical slices
    • Wu, J. Y., Guan, L. & Tsau, Y. (1999) Propagating activation during oscillations and evoked responses in neocortical slices. J. Neurosci., 19, 5005-5015.
    • (1999) J. Neurosci. , vol.19 , pp. 5005-5015
    • Wu, J.Y.1    Guan, L.2    Tsau, Y.3
  • 61
    • 0029961607 scopus 로고    scopus 로고
    • Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: A theory
    • Zhang, K. (1996) Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: A theory. J. Neurosci., 16, 2112-2126.
    • (1996) J. Neurosci. , vol.16 , pp. 2112-2126
    • Zhang, K.1
  • 62
    • 1042287949 scopus 로고    scopus 로고
    • On stability of traveling waves solutions in synaptically coupled neuronal networks
    • Zhang, L. (2003) On stability of traveling waves solutions in synaptically coupled neuronal networks. Differ. Integr. Equ., 16, 513-536.
    • (2003) Differ. Integr. Equ. , vol.16 , pp. 513-536
    • Zhang, L.1
  • 63
    • 1042291513 scopus 로고    scopus 로고
    • Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks
    • Zhang, L. (2004) Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks. J. Differ. Equ., 197, 162-196.
    • (2004) J. Differ. Equ. , vol.197 , pp. 162-196
    • Zhang, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.