EPJ Nonlinear Biomed Phys
Volume 2, Number 1, December 2014
Advances in Neural Population Models and Their Networks
Article Number 4
Number of page(s) 17
Published online 09 May 2014
  1. Wilson H, Cowan J: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.Kybernetik 1973, 13:55–80.
  2. Amari SI: Dynamics of pattern formation in lateral-inhibition type neural fields.Biol Cybern 1977, 27:77–87.
  3. Jancke D, Erlhagen W, Dinse HR, Akhavan AC, Giese M, Steinhage A, Schöner G: Parametric population representation of retinal location: neuronal interaction dynamics in cat primary visual cortex.J Neurosci 1999,19(20):9016–9028. []
  4. Bressloff PC: Spatiotemporal dynamics of continuum neural fields.J Phys A 2012,45(3):033001. []
  5. Coombes S: Large-scale neural dynamics: simple and complex.NeuroImage 2010,52(3):731–739. []
  6. Coombes S, Venkov NA, Shiau L, Bojak I, Liley DTJ, Laing CR: Modeling electrocortical activity through improved local approximations of integral neural field equations.Phys Rev E 2007,76(5):051901.
  7. Coombes S, Lord G, Owen M: Waves and bumps in neuronal networks with axo-dendritic synaptic interactions.Physica D 2003, 178:219–241.
  8. Folias S, Bressloff P: Stimulus-locked waves and breathers in an excitatory neural network.SIAM J Appl Math 2005, 65:2067–2092.
  9. Hutt A, Rougier N: Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields.Phys Rev E 2010, 82:R055701.
  10. Coombes S, Owen M: Bumps, breathers, and waves in a neural network with spike frequency adaptation.Phys Rev Lett 2005, 94:148102.
  11. Ermentrout GB, McLeod JB: Existence and uniqueness of travelling waves for a neural network.Proc R Soc E 1993, 123A:461–478.
  12. Jirsa VK, Haken H: Field theory of electromagnetic brain activity.Phys Rev Lett 1996,77(5):960–963.
  13. Hutt A: Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds.Phys Rev E 2007, 75:026214.
  14. Bressloff PC: Traveling fronts and wave propagation failure in an inhomogeneous neural network.Physica D 2001, 155:83–100.
  15. Jirsa VK, Kelso JAS: Spatiotemporal pattern formation in neural systems with heterogeneous connection toplogies.Phys Rev E 2000,62(6):8462–8465.
  16. Kilpatrick ZP, Folias SE, Bressloff PC: Traveling pulses and wave propagation failure in inhomogeneous neural media.SIAM J Appl Dynanmical Syst 2008, 7:161–185.
  17. Schmidt H, Hutt A, Schimansky-Geier L: Wave fronts in inhomogeneous neural field models.Physica D 2009,238(14):1101–1112.
  18. Potthast R, beim Graben P: Inverse problems in neural field theory.SIAM J Appl Dynamical Syst 2009,8(4):1405–1433.
  19. Potthast R, beim Graben P: Existence and properties of solutions for neural field equations.Math Methods Appl Sci 2010,33(8):935–949.
  20. Coombes S, Laing C, Schmidt H, Svanstedt N, Wyller J: Waves in random neural media.Discrete Contin Dyn Syst A 2012, 32:2951–2970.
  21. Coombes S, Laing C: Pulsating fronts in periodically modulated neural field models.Phys Rev E 2011, 83:011912.
  22. Brackley C, Turner M: Persistent fluctuations of activity in undriven continuum neural field models with power-law connections.Phys Rev E 2009, 79:011918.
  23. beim Graben P, Potthast R: Inverse problems in dynamic cognitive modeling.Chaos 2009, 19:015103.
  24. Hutt A, Riedel H: Analysis and modeling of quasi-stationary multivariate time series and their application to middle latency auditory evoked potentials.Physica D 2003,177(1–4):203–232.
  25. Yildiz I, Kiebel SJ: A hierarchical neuronal model for generation and online recognition of birdsongs.PloS Comput Biol 2011,7(12):e1002303.
  26. Veltz R, Faugeras O: Local/global analysis of the stationary solutions of some neural field equations.SIAM J Appl Dynamical Syst 2010, 9:954–998.
  27. Afraimovich VS, Zhigulin VP, Rabinovich MI: On the origin of reproducible sequential activity in neural circuits.Chaos 2004,14(4):1123–1129.
  28. Rabinovich MI, Huerta R, Varona P, Afraimovichs VS: Transient cognitive dynamics, metastability, and decision making.PLoS Comput Biolog 2008,4(5):e1000072.
  29. Hammerstein A: Nichtlineare Integralgleichungen nebst Anwendungen.Acta Math 1930, 54:117–176.
  30. Kosko B: Bidirectional associated memories.IEEE Trans Syst Man Cybernet 1988, 18:49–60.
  31. Hellwig B: A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex.Biol Cybernet 2000, 82:11–121.
  32. Mazor O, Laurent G: Transient dynamics versus fixed points in odor representations by locust antennal lobe projection neurons.Neuron 2005,48(4):661–673.
  33. Rabinovich MI, Huerta R, Laurent G: Transient dynamics for neural processing.Science 2008,321(5885):48–50.
  34. Kiebel SJ, von Kriegstein K, Daunizeau J, Friston KJ: Recognizing sequences of sequences.Plos Comp Biol 2009,5(8):e1000464.
  35. Desroches M, Guckenheimer J, Krauskopf B, Kuehn C, Osinga H, Wechselberger M: Mixed-mode oscillations with multiple time scales.SIAM Rev 2012,54(2):211–288. []
  36. Tsuda I: Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems.Behav Brain Sci 2001,24(5):793–847.
  37. Freeman W: Evidence from human scalp EEG of global chaotic itinerancy.Chaos 2003,13(3):1069.
  38. Appell J, Chen CJ: How to solve Hammerstein equations.J Integr Equat Appl 2006,18(3):287–296.
  39. Banas J: Integrable solutions of Hammerstein and Urysohn integral equations.J Austral Math Soc (Series A) 1989, 46:61–68.
  40. Lakestani M, Razzaghi M, Dehghan M: Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets.Math Problems Eng 2005, 113–121.
  41. Djitteab N, Senea M: An iterative algorithm for approximating solutions of Hammerstein integral equations.Numerical Funct Anal Optimization 2013,34(12):1299–1316.
  42. Hutt A, Longtin A: Effects of the anesthetic agent propofol on neural populations.Cogn Neurodyn 2010, 4:37–59.
  43. Bressloff PC, Coombes S: Physics of the extended neuron.Int J Mod Phys 1997,B 11(20):2343–2392.
  44. beim Graben P, Potthast R: A dynamic field account to language-related brain potentials. In Principles of Brain Dynamics: Global State Interactions. Edited by: Rabinovich M, Friston K, Varona P. Cambridge (MA): MIT Press; 2012:93–112.
  45. Haken H: Synergetics. An Introduction Volume 1 of Springer Series in Synergetics. Berlin: Springer; 1983. [1st edition 1977]
  46. Fukai T, Tanaka S: A simple neural network exhibiting selective activation of neuronal ensembles: from winner-take-all to winners-share-all.Neural Comp 1997, 9:77–97. []
  47. Wilson H, Cowan J: Excitatory and inhibitory interactions in localized populations of model neurons.Biophys J 1972, 12:1–24.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.