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第90行： − − <br style="clear:both;" /> − − == 参考文献== − *S Amari. Dynamics of pattern formation in lateral inhibition type neural fields. Biological Cybernetics, 27:77–87, 1977. − *S Amari. Homogeneous nets of neuron-like elements. Biological Cybernetics, 17:211–220, 1975. − * F.M. Atay and A.Hutt, Neural fields with distributed transmission speeds and long-range feedback delays. SIAM Journal Applied Dynamical Systems 5(4), 670-698, 2006 − *R Ben-Yishai, L Bar-Or, and H Sompolinsky. Theory of orientation tuning in visual cortex. Proceedings of the National Academy of Sciences USA, 92:3844–3848, 1995. − * R L Beurle. Properties of a mass of cells capable of regenerating pulses. Philosophical Transactions of the Royal Society London B, 240:55–94, 1956. − *W H Bosking, Y Zhang, B Schofield and D Fitzpatrick. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci., 17:2112-2127, 1997. − * P C Bressloff. Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D, 155:83-100, 2001. − *P C Bressloff, J D Cowan, M Golubitsky, P J Thomas and M Wiener. Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. Phil. Trans. Roy. Soc. B, 356: 299-330. − *P C Bressloff. Stochastic neural field theory and the system-size expansion. SIAM J. Applied Mathematics, 70:1488-1521, 2009 − *M Camperi and X-J Wang. A model of visuospatial short-term memory in prefrontal cortex: recurrent network and cellular bistability. J. Comp. Neurosci., 5:383-405, 1998. − *R D Chervin, P A Pierce, and BWConnors. Periodicity and directionality in the propagation of epileptiform discharges across neortex. Journal of Neurophysiology, 60:1695–1713, 1988. − *B W Connors and Y Amitai. Generation of epileptiform discharges by local circuits in neocortex. In P A Schwartzkroin, editor, Epilepsy: Models, Mechanisms and Concepts, pages 388–424. Cambridge University Press, 1993. − *C L Colby, J R Duhamel, and M E Goldberg. Oculocentric spatial representation in parietal cortex. Cerebral Cortex, 5:470–481, 1995. − *S Coombes and M R Owen. Evans functions for integral neural field equations with Heaviside firing rate function. SIAM Journal on Applied Dynamical Systems, 34:574–600, 2004. − *S Coombes and M R Owen. Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters, 94, 148102, 2005. − *G B Ermentrout and J D Cowan. A mathematical theory of visual hallucination patterns. Biological Cybernetics, 34:137–150, 1979. − *G B Ermentrout and J B McLeod. Existence and uniqueness of travelling waves for a neural network. Proceedings of the Royal Society of Edinburgh, 123A:461–478, 1993. − *G B Ermentrout and D Kleinfeld. Traveling electrical waves in cortex: Insights from phase dynamics and speculation on a computational role. Neuron, 29:33–44, 2001. − *J Evans. Nerve axon equations: IV The stable and unstable impulse. Indiana University Mathematics Journal, 24:1169–1190, 1975. − *C P Fall, T J Lewis and J Rinzel. Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability. Biological Cybernetics, 93:109-18, 2004. − * O Faugeras, J Touboul and B Cessac. A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs. Frontiers of Computational Neuroscience, 3:1, 2009 − *S E Folias and P C Bressloff. Breathing pulses in an excitatory neural network. SIAM J. Appl. Dyn. Syst., 3:378-407, 2004. − *J S Griffith. A field theory of neural nets: I: Derivation of field equations. Bulletin of Mathematical Biophysics, 25:111–120, 1963. − *J S Griffith. A field theory of neural nets: II: Properties of field equations. Bulletin of Mathematical Biophysics, 27:187–195, 1965. − *P S Goldman-Rakic. Cellular basis of working memory. Neuron, 14:477–485, 1995. − *D Golomb and Y Amitai. Propagating neuronal discharges in neocortical slices: Computational and experimental study. Journal of Neurophysiology, 78:1199–1211, 1997. − * D H Hubel and T N Wiesel. Receptive Fields, Binocular Interaction And Functional Architecture In The Cat's Visual Cortex. Journal of Physiology 160:106–154, 1962 − * V K Jirsa and H Haken. A derivation of a macroscopic field theory of the brain from the quasi-microscopic neural dynamics. Physica D, 99:503–526, 1997. − *U Kim, T Bal, and D A McCormick. Spindle waves are propagating synchronized oscillations in the ferret LGNd in vitro. Journal of Neurophysiology, 74:1301–1323, 1995. − *K Kishimoto and S Amari. Existence and stability of local excitations in homogeneous neural fields. Journal of Mathematical Biology, 7:303–318, 1979. − * C R Laing. Spiral waves in nonlocal equations. SIAM Journal on Applied Dynamical Systems, 4:588-606, 2005. − *C R laing and C C Chow. Stationary bumps in networks of spiking neurons. Neural Comput., 13:1473–1494, 2001. − * C R Laing and W C Troy. PDE methods for nonlocal models. SIAM Journal on Applied Dynamical Systems, 2:487–516, 2003. − *P Tass. Cortical pattern formation during visual hallucinations. Journal of Biological Physics, 21:177–210, 1995. − * R Miles, R D Traub, and R K S Wong. Spread of synchronous firing in longitudinal slices from the CA3 region of Hippocampus. Journal of Neurophysiology, 60:1481–1496, 1995. − * P L Nunez. The brain wave equation: a model for the EEG. Mathematical Biosciences, 21:279–297, 1974. − *C C Petersen. The functional organization of the barrel cortex. Neuron 56(2):339-55, 2007. − *D J Pinto and G B Ermentrout. Spatially structured activity in synaptically coupled neuronal networks: I. Travelling fronts and pulses. SIAM Journal on Applied Mathematics, 62:206–225, 2001. − * K A Richardson, S J Schiff, and B J Gluckman. Control of traveling waves in the mammalian cortex. Physical Review Letters, 94:028103, 2005. − * J A Saez, J Paniagua, I Dominguez & J M Ferrer. Image processing in the primary visual cortex. Review Neurology 26(151):439-44, 1998. − *D C Somers, S B Nelson and M Sur. An emergent model of orientation selectivity in cat visual cortical simple cells. Journal of Neuroscience 15(8), 5448-5465, 1995 − *H R Wilson and J D Cowan. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12:1–24, 1972. − *H R Wilson and J D Cowan. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13:55–80, 1973. − *J Y Wu, L Guan, and Y Tsau. Propagating activation during oscillations and evoked responses in neocortical slices. Journal of Neuroscience, 19:5005–5015, 1999. − *K Zhang. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. Journal of Neuroscience, 16:2112–2126, 1996. − − <!-- Authors, please check this list and remove any references that are irrelevant. This list is generated automatically to reflect the links from your article to other accepted articles in Scholarpedia. --> − <b>Internal references</b> − − *Yuri A. Kuznetsov (2006) [[Andronov-Hopf bifurcation]]. Scholarpedia, 1(10):1858. − *John W. Milnor (2006) [[Attractor]]. Scholarpedia, 1(11):1815. − *Eugene M. Izhikevich (2006) [[Bursting]]. Scholarpedia, 1(3):1300. − *Philip Holmes and Eric T. Shea-Brown (2006) [[Stability]]. Scholarpedia, 1(10):1838. − *S. Murray Sherman (2006) [[Thalamus]]. Scholarpedia, 1(9):1583. 第183行：
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无编辑摘要
大多数神经场模型中的一个常见假设是网络是同质的和各向同性的，也就是说，权重分布取决于网络内交互种群之间的距离。然而，由于在皮层表层中发现的长程水平连接的斑块性质，真正的皮层更现实地被建模为各向异性和不均匀的二维介质（Bosking et al. 1997<ref>W H Bosking, Y Zhang, B Schofield and D Fitzpatrick. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci., 17:2112-2127, 1997.</ref>）。重量分布的各向异性可能导致不同方向的波速变化，而不均匀性可能导致随时间变化的波剖面，并可能导致波传播失败（Bressloff 2001<ref>P C Bressloff. Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D, 155:83-100, 2001.</ref>）。
大多数神经场模型中的一个常见假设是网络是同质的和各向同性的，也就是说，权重分布取决于网络内交互种群之间的距离。然而，由于在皮层表层中发现的长程水平连接的斑块性质，真正的皮层更现实地被建模为各向异性和不均匀的二维介质（Bosking et al. 1997<ref>W H Bosking, Y Zhang, B Schofield and D Fitzpatrick. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci., 17:2112-2127, 1997.</ref>）。重量分布的各向异性可能导致不同方向的波速变化，而不均匀性可能导致随时间变化的波剖面，并可能导致波传播失败（Bressloff 2001<ref>P C Bressloff. Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D, 155:83-100, 2001.</ref>）。
==外部链接==
==外部链接==
[[Category: Dynamical Systems]]
[[Category: Dynamical Systems]]
[[Category: Neural Networks]]
[[Category: Neural Networks]]
== 参考文献==
<references /><b>Internal references</b>
*Yuri A. Kuznetsov (2006) [[Andronov-Hopf bifurcation]]. Scholarpedia, 1(10):1858.
*John W. Milnor (2006) [[Attractor]]. Scholarpedia, 1(11):1815.
*Eugene M. Izhikevich (2006) [[Bursting]]. Scholarpedia, 1(3):1300.
*Philip Holmes and Eric T. Shea-Brown (2006) [[Stability]]. Scholarpedia, 1(10):1838.
*S. Murray Sherman (2006) [[Thalamus]]. Scholarpedia, 1(9):1583.
参考 http://www.scholarpedia.org/article/Neural_fields
参考 http://www.scholarpedia.org/article/Neural_fields