Skip to main content
Erschienen in: Journal of Computational Neuroscience 2/2010

01.04.2010

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

verfasst von: Zachary P. Kilpatrick, Paul C. Bressloff

Erschienen in: Journal of Computational Neuroscience | Ausgabe 2/2010

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synaptic depression and cortical gain control. Science, 275, 220–224.CrossRefPubMed Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synaptic depression and cortical gain control. Science, 275, 220–224.CrossRefPubMed
Zurück zum Zitat Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27, 77–87.CrossRefPubMed Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27, 77–87.CrossRefPubMed
Zurück zum Zitat Bao, S., Chang, E. F., Davis, J. D., Gobeske, K. T., & Merzenich, M. M. (2003). Progressive degradation and subsequent refinement of acoustic representations in the adult auditory cortex. Journal of Neuroscience, 23, 10765–10775.PubMed Bao, S., Chang, E. F., Davis, J. D., Gobeske, K. T., & Merzenich, M. M. (2003). Progressive degradation and subsequent refinement of acoustic representations in the adult auditory cortex. Journal of Neuroscience, 23, 10765–10775.PubMed
Zurück zum Zitat Bart, E., Bao, S., & Holcman, D. (2005). Modeling the spontaneous activity of the auditory cortex. Journal of Computational Neuroscience, 19, 357–378.CrossRefPubMed Bart, E., Bao, S., & Holcman, D. (2005). Modeling the spontaneous activity of the auditory cortex. Journal of Computational Neuroscience, 19, 357–378.CrossRefPubMed
Zurück zum Zitat Benda, J., & Herz, A. V. M. (2003). A universal model for spike-frequency adaptation. Neural Computation, 15, 2523–2564.CrossRefPubMed Benda, J., & Herz, A. V. M. (2003). A universal model for spike-frequency adaptation. Neural Computation, 15, 2523–2564.CrossRefPubMed
Zurück zum Zitat Benucci, A., Frazor, R. A., & Carandini, M. (2007). Standing waves and traveling waves distinguish two circuits in visual cortex. Neuron, 55, 103–117.CrossRefPubMed Benucci, A., Frazor, R. A., & Carandini, M. (2007). Standing waves and traveling waves distinguish two circuits in visual cortex. Neuron, 55, 103–117.CrossRefPubMed
Zurück zum Zitat Buszaki, G. (2006). Rhythms of the brain. Oxford: Oxford University Press.CrossRef Buszaki, G. (2006). Rhythms of the brain. Oxford: Oxford University Press.CrossRef
Zurück zum Zitat Buszaki, G., & Draguhn, A. (2004). Neuronal oscillation in cortical networks. Science, 304, 1926–1929.CrossRef Buszaki, G., & Draguhn, A. (2004). Neuronal oscillation in cortical networks. Science, 304, 1926–1929.CrossRef
Zurück zum Zitat Chervin, R. D., Pierce, P. A., & Connors, B. W. (1988). Periodicity and directionality in the propagation of epileptiform discharges across neocortex. Journal of Neurophysiology, 60, 1695–1713.PubMed Chervin, R. D., Pierce, P. A., & Connors, B. W. (1988). Periodicity and directionality in the propagation of epileptiform discharges across neocortex. Journal of Neurophysiology, 60, 1695–1713.PubMed
Zurück zum Zitat Delaney, K., Gelperin, A., Fee, M., Flores, J., Gervais, R., & Tank, D. (1994). Waves and stimulus-modulated dynamics in an oscillating olfactory network. Proceedings of the National Academy of Sciences of the United States of America, 91, 669–73.CrossRefPubMed Delaney, K., Gelperin, A., Fee, M., Flores, J., Gervais, R., & Tank, D. (1994). Waves and stimulus-modulated dynamics in an oscillating olfactory network. Proceedings of the National Academy of Sciences of the United States of America, 91, 669–73.CrossRefPubMed
Zurück zum Zitat Dudek, F. E., & Spitz, M. (1997). Hypothetical mechanisms for the cellular and neurophysiological basis of secondary epileptogenesis: Proposed role for synaptic reorganization. Journal of Clinical Neurophysiology, 14, 90–101.CrossRefPubMed Dudek, F. E., & Spitz, M. (1997). Hypothetical mechanisms for the cellular and neurophysiological basis of secondary epileptogenesis: Proposed role for synaptic reorganization. Journal of Clinical Neurophysiology, 14, 90–101.CrossRefPubMed
Zurück zum Zitat Ermentrout, G. B. (1998). Linearization of f-I curves by adaptation. Neural Computation, 10, 1721–1729.CrossRefPubMed Ermentrout, G. B. (1998). Linearization of f-I curves by adaptation. Neural Computation, 10, 1721–1729.CrossRefPubMed
Zurück zum Zitat Ermentrout, G. B., & Kleinfeld, D. (2001). Traveling electrical waves in cortex: Insights from phase dynamics and speculation on a computational role. Neuron, 29, 33–44.CrossRefPubMed Ermentrout, G. B., & Kleinfeld, D. (2001). Traveling electrical waves in cortex: Insights from phase dynamics and speculation on a computational role. Neuron, 29, 33–44.CrossRefPubMed
Zurück zum Zitat Folias, S. E., & Bressloff, P. C. (2004). Breathing pulses in an excitatory neural network. SIAM Journal on Applied Dynamical Systems, 3, 378–407.CrossRef Folias, S. E., & Bressloff, P. C. (2004). Breathing pulses in an excitatory neural network. SIAM Journal on Applied Dynamical Systems, 3, 378–407.CrossRef
Zurück zum Zitat Folias, S. E., & Bressloff, P. C. (2005a). Breathers in two-dimensional neural media. Physical Review Letters, 95, 208107.CrossRefPubMed Folias, S. E., & Bressloff, P. C. (2005a). Breathers in two-dimensional neural media. Physical Review Letters, 95, 208107.CrossRefPubMed
Zurück zum Zitat Folias, S. E., & Bressloff, P. C. (2005b). Stimulus-locked traveling waves and breathers in an excitatory neural network. SIAM journal on Applied Mathematics, 65, 2067–2092.CrossRef Folias, S. E., & Bressloff, P. C. (2005b). Stimulus-locked traveling waves and breathers in an excitatory neural network. SIAM journal on Applied Mathematics, 65, 2067–2092.CrossRef
Zurück zum Zitat Fung, C. C. A., Wong, K. Y. M., & Wu, S. (2008). Dynamics of neural networks with continuous attractors. EPL, 84, 18002.CrossRef Fung, C. C. A., Wong, K. Y. M., & Wu, S. (2008). Dynamics of neural networks with continuous attractors. EPL, 84, 18002.CrossRef
Zurück zum Zitat Guo, Y., & Chow, C. C. (2005a). Existence and stability of standing pulses in neural networks: I. Existence. SIAM Journal on Applied Dynamical Systems, 4, 217–248.CrossRef Guo, Y., & Chow, C. C. (2005a). Existence and stability of standing pulses in neural networks: I. Existence. SIAM Journal on Applied Dynamical Systems, 4, 217–248.CrossRef
Zurück zum Zitat Guo, Y., & Chow, C. C. (2005b). Existence and stability of standing pulses in neural networks: II. Stability. SIAM Journal on Applied Dynamical Systems, 4, 249–281.CrossRef Guo, Y., & Chow, C. C. (2005b). Existence and stability of standing pulses in neural networks: II. Stability. SIAM Journal on Applied Dynamical Systems, 4, 249–281.CrossRef
Zurück zum Zitat Han, F., Caporale, N., & Dan, Y. (2008). Reverberation of recent visual experience in spontaneous cortical waves. Neuron, 60, 321–327.CrossRefPubMed Han, F., Caporale, N., & Dan, Y. (2008). Reverberation of recent visual experience in spontaneous cortical waves. Neuron, 60, 321–327.CrossRefPubMed
Zurück zum Zitat Hansel, D., & Sompolinsky, H. (2001). Methods in neuronal modeling. In Modeling feature selectivity in local cortical circuits (2nd Ed., ch. 13, pp. 499–568). Cambridge: MIT. Hansel, D., & Sompolinsky, H. (2001). Methods in neuronal modeling. In Modeling feature selectivity in local cortical circuits (2nd Ed., ch. 13, pp. 499–568). Cambridge: MIT.
Zurück zum Zitat Holcman, D., & Tsodyks, M. (2006). The emergence of Up and Down states in cortical networks. PLoS Computational Biology, 2, 174–181.CrossRef Holcman, D., & Tsodyks, M. (2006). The emergence of Up and Down states in cortical networks. PLoS Computational Biology, 2, 174–181.CrossRef
Zurück zum Zitat Huang, X., Troy, W. C., Yang, Q., Ma, H., Laing, C. R., Schiff, S. J., et al. (2004). Spiral waves in disinhibited mammalian neocortex. Journal of Neuroscience, 24, 9897–9902.CrossRefPubMed Huang, X., Troy, W. C., Yang, Q., Ma, H., Laing, C. R., Schiff, S. J., et al. (2004). Spiral waves in disinhibited mammalian neocortex. Journal of Neuroscience, 24, 9897–9902.CrossRefPubMed
Zurück zum Zitat Hutt, A., Longtin, A., & Schimansky-Geier, L. (2008). Additive noise-induces Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation. Physica D, 237, 755–773.CrossRef Hutt, A., Longtin, A., & Schimansky-Geier, L. (2008). Additive noise-induces Turing transitions in spatial systems with application to neural fields and the Swift-Hohenberg equation. Physica D, 237, 755–773.CrossRef
Zurück zum Zitat Jung, P., & Mayer-Kress, G. (1995). Spatiotemporal stochastic resonance in excitable media. Physical Review Letters, 74, 2130–2133.CrossRefPubMed Jung, P., & Mayer-Kress, G. (1995). Spatiotemporal stochastic resonance in excitable media. Physical Review Letters, 74, 2130–2133.CrossRefPubMed
Zurück zum Zitat Klimesch, W. (1999). EEG alpha and theta oscillations reflect cognitive and memory performance: A review and analysis. Brain Research Reviews, 29, 169–195.CrossRefPubMed Klimesch, W. (1999). EEG alpha and theta oscillations reflect cognitive and memory performance: A review and analysis. Brain Research Reviews, 29, 169–195.CrossRefPubMed
Zurück zum Zitat Laing, C. R. (2005). Spiral waves in nonlocal equations. SIAM Journal on Applied Dynamical Systems, 4, 588–606.CrossRef Laing, C. R. (2005). Spiral waves in nonlocal equations. SIAM Journal on Applied Dynamical Systems, 4, 588–606.CrossRef
Zurück zum Zitat Laing, C. R., Frewen, T. A., & Kevrekidis, I. G. (2007). Coarse-grained dynamics of an activity bump in a neural field model. Nonlinearity, 20, 2127–2146.CrossRef Laing, C. R., Frewen, T. A., & Kevrekidis, I. G. (2007). Coarse-grained dynamics of an activity bump in a neural field model. Nonlinearity, 20, 2127–2146.CrossRef
Zurück zum Zitat Laing, C. R., & Troy, W. C. (2003). PDE methods for nonlocal models. SIAM Journal on Applied Dynamical Systems, 2, 487–516.CrossRef Laing, C. R., & Troy, W. C. (2003). PDE methods for nonlocal models. SIAM Journal on Applied Dynamical Systems, 2, 487–516.CrossRef
Zurück zum Zitat Lakatos, P., Chen, C. M., O’Connell, M. N., Mills, A., & Schroeder, C. E. (2007). Neuronal oscillations and multisensory interaction in primary auditory cortex. Neuron, 53, 279–292.CrossRefPubMed Lakatos, P., Chen, C. M., O’Connell, M. N., Mills, A., & Schroeder, C. E. (2007). Neuronal oscillations and multisensory interaction in primary auditory cortex. Neuron, 53, 279–292.CrossRefPubMed
Zurück zum Zitat Lam, Y. W., Cohen, L. B., Wachowiak, M., & Zochowski, M. R. (2000). Odors elicit three different oscillations in the turtle olfactory bulb. Journal of Neuroscience, 20, 749–62.PubMed Lam, Y. W., Cohen, L. B., Wachowiak, M., & Zochowski, M. R. (2000). Odors elicit three different oscillations in the turtle olfactory bulb. Journal of Neuroscience, 20, 749–62.PubMed
Zurück zum Zitat Lee, U., Kim, S., & Jung, K. Y. (2006). Classification of epilepsy types through global network analysis of scalp electroencephalograms. Physical Review E, 73, 041920.CrossRef Lee, U., Kim, S., & Jung, K. Y. (2006). Classification of epilepsy types through global network analysis of scalp electroencephalograms. Physical Review E, 73, 041920.CrossRef
Zurück zum Zitat Linder, B., Garcia-Ojalvo, J., Neiman, A., & Schimansky-Geier, L. (2004). Effects of noise in excitable systems. Physics Reports, 393, 321–424.CrossRef Linder, B., Garcia-Ojalvo, J., Neiman, A., & Schimansky-Geier, L. (2004). Effects of noise in excitable systems. Physics Reports, 393, 321–424.CrossRef
Zurück zum Zitat Matveev, V., & Wang, X. J. (2000). Implications of all-or-none synaptic transmission and short-term depression beyond vesicle depletion: A computational study. Journal of Neuroscience, 20, 1575–1588.PubMed Matveev, V., & Wang, X. J. (2000). Implications of all-or-none synaptic transmission and short-term depression beyond vesicle depletion: A computational study. Journal of Neuroscience, 20, 1575–1588.PubMed
Zurück zum Zitat McNamara, J. O. (1994). Cellular and molecular basis of epilepsy. Journal of Neuroscience, 14, 3412–3425. McNamara, J. O. (1994). Cellular and molecular basis of epilepsy. Journal of Neuroscience, 14, 3412–3425.
Zurück zum Zitat Melamed, O., Barak, O., Silberberg, G., Markram, H., & Tsodyks, M. (2008). Slow oscillations in neural networks with facilitating synapses, Journal of Computational Neuroscience, 25, 308–316.CrossRefPubMed Melamed, O., Barak, O., Silberberg, G., Markram, H., & Tsodyks, M. (2008). Slow oscillations in neural networks with facilitating synapses, Journal of Computational Neuroscience, 25, 308–316.CrossRefPubMed
Zurück zum Zitat Milton, J., & Jung, P. (2003). Epilepsy as a dynamic disease. Berlin: Springer. Milton, J., & Jung, P. (2003). Epilepsy as a dynamic disease. Berlin: Springer.
Zurück zum Zitat Milton, J. G., Chu, P. H., & Cowan, J. D. (1993). Spiral waves in integrate-and-fire neural etworks. In S. J. Hanson, J. D. Cowan, & C. L. Giles (Eds.), Advances in neural information n processing systems (pp. 1001–1007). San Mateo: Morgan Kaufmann. Milton, J. G., Chu, P. H., & Cowan, J. D. (1993). Spiral waves in integrate-and-fire neural etworks. In S. J. Hanson, J. D. Cowan, & C. L. Giles (Eds.), Advances in neural information n processing systems (pp. 1001–1007). San Mateo: Morgan Kaufmann.
Zurück zum Zitat Owen, M. R., Laing, C. R., & Coombes, S. (2007). Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9, 378.CrossRef Owen, M. R., Laing, C. R., & Coombes, S. (2007). Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9, 378.CrossRef
Zurück zum Zitat Petersen, C. C. H., Grinvald, A., & Sakmann, B. (2003). Spatiotemporal dynamics of sensory responses in layer 2/3 of rat barrel cortex measured in vivo by voltage-sensitive dye imaging combined with whole-cell voltage recordings and neuron reconstructions. Journal of Neuroscience, 23(4), 1298–1309.PubMed Petersen, C. C. H., Grinvald, A., & Sakmann, B. (2003). Spatiotemporal dynamics of sensory responses in layer 2/3 of rat barrel cortex measured in vivo by voltage-sensitive dye imaging combined with whole-cell voltage recordings and neuron reconstructions. Journal of Neuroscience, 23(4), 1298–1309.PubMed
Zurück zum Zitat Pinto, D. J., & Ermentrout, G. B. (2001a). Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses. SIAM journal on Applied Mathematics, 62, 206–225.CrossRef Pinto, D. J., & Ermentrout, G. B. (2001a). Spatially structured activity in synaptically coupled neuronal networks: I. Traveling fronts and pulses. SIAM journal on Applied Mathematics, 62, 206–225.CrossRef
Zurück zum Zitat Pinto, D. J., & Ermentrout, G. B. (2001b). Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses. SIAM Journal on Applied Mathematics, 62, 226–243.CrossRef Pinto, D. J., & Ermentrout, G. B. (2001b). Spatially structured activity in synaptically coupled neuronal networks: II. Lateral inhibition and standing pulses. SIAM Journal on Applied Mathematics, 62, 226–243.CrossRef
Zurück zum Zitat Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P., & Kleinfeld, D. (1997). Visual stimuli induce waves of electrical activity in turtle cortex. Proceedings of the National Academy of Sciences of the United States of America, 94, 7621–7626.CrossRefPubMed Prechtl, J. C., Cohen, L. B., Pesaran, B., Mitra, P. P., & Kleinfeld, D. (1997). Visual stimuli induce waves of electrical activity in turtle cortex. Proceedings of the National Academy of Sciences of the United States of America, 94, 7621–7626.CrossRefPubMed
Zurück zum Zitat Roelfsema, P. R., Engel, A. K., Konig, P., & Singer, W. (1997). Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature, 385, 1157–1161.CrossRef Roelfsema, P. R., Engel, A. K., Konig, P., & Singer, W. (1997). Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature, 385, 1157–1161.CrossRef
Zurück zum Zitat Rubin, J., & Bose, A. (2004). Localized activity patterns in excitatory neuronal networks. Network, 15, 133–158.CrossRefPubMed Rubin, J., & Bose, A. (2004). Localized activity patterns in excitatory neuronal networks. Network, 15, 133–158.CrossRefPubMed
Zurück zum Zitat Schiff, S. J., Huang, X., & Wu, J. Y. (2007). Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. Physical Review Letters, 98, 178102.CrossRefPubMed Schiff, S. J., Huang, X., & Wu, J. Y. (2007). Dynamical evolution of spatiotemporal patterns in mammalian middle cortex. Physical Review Letters, 98, 178102.CrossRefPubMed
Zurück zum Zitat Schiff, S. J., Sauer, T., Kumar, R., & Weinstein, S. L. (2005). Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures. Neuroimage, 28, 1043–1055.CrossRefPubMed Schiff, S. J., Sauer, T., Kumar, R., & Weinstein, S. L. (2005). Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures. Neuroimage, 28, 1043–1055.CrossRefPubMed
Zurück zum Zitat Sederberg, P. B., Kahana, M. J., Howard, M. W., Donner, E. J., & Madsen, J. R. (2003). Theta and gamma oscillations during encoding predict subsequent recall. Journal of Neuroscience, 23, 10809–10814.PubMed Sederberg, P. B., Kahana, M. J., Howard, M. W., Donner, E. J., & Madsen, J. R. (2003). Theta and gamma oscillations during encoding predict subsequent recall. Journal of Neuroscience, 23, 10809–10814.PubMed
Zurück zum Zitat Shusterman, V., & Troy, W. C. (2008). From baseline to epileptiform activity: A path to synchronized rhythmicity in large-scale neural networks. Physical Review E, 77, 061911.CrossRef Shusterman, V., & Troy, W. C. (2008). From baseline to epileptiform activity: A path to synchronized rhythmicity in large-scale neural networks. Physical Review E, 77, 061911.CrossRef
Zurück zum Zitat Singer, W., & Gray, C. M. (1995). Visual feature integration and the temporal correlation hypothesis. Annual Review of Neuroscience, 18, 555–586.CrossRefPubMed Singer, W., & Gray, C. M. (1995). Visual feature integration and the temporal correlation hypothesis. Annual Review of Neuroscience, 18, 555–586.CrossRefPubMed
Zurück zum Zitat Stevens, C., & Wesseling, J. (1998). Activity-dependent modulation of the rate at which synaptic vesicles become available to undergo exocytosis. Neuron, 21, 415–424.CrossRefPubMed Stevens, C., & Wesseling, J. (1998). Activity-dependent modulation of the rate at which synaptic vesicles become available to undergo exocytosis. Neuron, 21, 415–424.CrossRefPubMed
Zurück zum Zitat Tabak, J., Senn, W., O’Donovan, M. J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. Journal of Neuroscience, 20, 3041–3056.PubMed Tabak, J., Senn, W., O’Donovan, M. J., & Rinzel, J. (2000). Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network. Journal of Neuroscience, 20, 3041–3056.PubMed
Zurück zum Zitat Troy, W. C. (2008). Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections. SIAM Journal on Applied Dynamical Systems, 7, 1247–1282.CrossRef Troy, W. C. (2008). Traveling waves and synchrony in an excitable large-scale neuronal network with asymmetric connections. SIAM Journal on Applied Dynamical Systems, 7, 1247–1282.CrossRef
Zurück zum Zitat Troy, W. C., & Shusterman, V. (2007). Patterns and features of families of traveling waves in large-scale neuronal networks. SIAM Journal on Applied Dynamical Systems, 6, 263–292.CrossRef Troy, W. C., & Shusterman, V. (2007). Patterns and features of families of traveling waves in large-scale neuronal networks. SIAM Journal on Applied Dynamical Systems, 6, 263–292.CrossRef
Zurück zum Zitat Tsodyks, M. S., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences of the United States of America, 94, 719–723.CrossRefPubMed Tsodyks, M. S., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences of the United States of America, 94, 719–723.CrossRefPubMed
Zurück zum Zitat Tsodyks, M. S., Pawelzik, K., & Markram, H. (1998). Neural networks with dynamic synapses. Neural Computation, 10, 821–835.CrossRefPubMed Tsodyks, M. S., Pawelzik, K., & Markram, H. (1998). Neural networks with dynamic synapses. Neural Computation, 10, 821–835.CrossRefPubMed
Zurück zum Zitat Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. Journal of Neurophysiology, 79, 1549–1566.PubMed Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. Journal of Neurophysiology, 79, 1549–1566.PubMed
Zurück zum Zitat Wang, X. J. (1999). Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. Journal of Neuroscience, 19, 9587–9603.PubMed Wang, X. J. (1999). Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. Journal of Neuroscience, 19, 9587–9603.PubMed
Zurück zum Zitat Wu, J. Y. (2008). Propagating waves of activity in the neocortex: What they are, what they do. Neuroscientist, 14, 487–502.CrossRefPubMed Wu, J. Y. (2008). Propagating waves of activity in the neocortex: What they are, what they do. Neuroscientist, 14, 487–502.CrossRefPubMed
Zurück zum Zitat Wu, J. Y., Guan, L., & Tsau, Y. (1999). Propagating activation during oscillations and evoked responses in neocortical slices. Journal of Neuroscience, 19, 5005–5015.PubMed Wu, J. Y., Guan, L., & Tsau, Y. (1999). Propagating activation during oscillations and evoked responses in neocortical slices. Journal of Neuroscience, 19, 5005–5015.PubMed
Zurück zum Zitat Wu, S., Hamaguchi, K., & Amari, S.-I. (2008). Dynamics and computation of continuous attractors. Neural Computation, 20, 994–1025.CrossRefPubMed Wu, S., Hamaguchi, K., & Amari, S.-I. (2008). Dynamics and computation of continuous attractors. Neural Computation, 20, 994–1025.CrossRefPubMed
Zurück zum Zitat Xu, W., Huang, X., Takagaki, K., & Wu, J. Y. (2007). Compression and reflection of visually evoked cortical waves. Neuron, 55, 119–129.CrossRefPubMed Xu, W., Huang, X., Takagaki, K., & Wu, J. Y. (2007). Compression and reflection of visually evoked cortical waves. Neuron, 55, 119–129.CrossRefPubMed
Zurück zum Zitat Zucker, R. S., & Regehr, W. G. (2002). Short-term synaptic plasticity. Annual Review of Physiology, 64, 355–405.CrossRefPubMed Zucker, R. S., & Regehr, W. G. (2002). Short-term synaptic plasticity. Annual Review of Physiology, 64, 355–405.CrossRefPubMed
Metadaten
Titel
Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression
verfasst von
Zachary P. Kilpatrick
Paul C. Bressloff
Publikationsdatum
01.04.2010
Verlag
Springer US
Erschienen in
Journal of Computational Neuroscience / Ausgabe 2/2010
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI
https://doi.org/10.1007/s10827-009-0199-6

Weitere Artikel der Ausgabe 2/2010

Journal of Computational Neuroscience 2/2010 Zur Ausgabe

Premium Partner