Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 2, 2010
Mathematics and neuroscience
|
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Page(s) | 5 - 25 | |
DOI | https://doi.org/10.1051/mmnp/20105201 | |
Published online | 10 March 2010 |
- O. Bennani, G. Chauvet, P. Chauvet, J.M. Dupont, F. Jouen. A hierarchical modeling approach of hippocampus local circuit. J. Integr. Neurosci., 9 (2009), 49–76. [CrossRef] [Google Scholar]
- G.A. Chauvet. The use of representation and formalism in a theoretical approach to integrative neuroscience. J. Integr. Neurosci., 4 (2005), 291–312. [CrossRef] [PubMed] [Google Scholar]
- C. Dejean, C.E. Gross, B. Bioulac, T. Boraud. Dynamic changes in the cortex-basal ganglia network after dopamine depletion in the rat. J. Neurophysiol., 100 (2008), 385–396. [CrossRef] [PubMed] [Google Scholar]
- O. Faugeras, F. GrimbertJ.-J. Slotine. Absolute stability and complete synchronization in a class of neural fields models. SIAM J. Appl. Math., 61 (2008), No. 1, 205-250. [CrossRef] [Google Scholar]
- F. C. Hoppensteadt, E. Izhikevich. Weakly connected neural networks. Springer-Verlag, New York, 1997. [Google Scholar]
- E. M. Izhikevich. Dynamical Systems in Neuroscience: The geometry of excitability and bursting. The MIT Press, 2007. [Google Scholar]
- E. M. Izhikevich. Phase equations for relaxation oscillators. SIAM J. Appl. Math., 60 (2000), 1789-1804. [CrossRef] [MathSciNet] [Google Scholar]
- E.M. Izhikevich. Which model to use for cortical spiking neurons?. IEEE Trans Neural Netw, 15 (2004), 1063–1070. [Google Scholar]
- N. Koppel, G.B. Ermentrout. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. Handbook of Dynamical Systems, 2 (2002), 3–54. [CrossRef] [Google Scholar]
- G. S. Medvedev, N. Koppel. Synchronization and transient dynamics in the chains of electrically coupled Fitzhugh-Nagumo oscillators. SIAM J. Appl. Math., 60 (2001), No. 5, 1762–1801. [CrossRef] [Google Scholar]
- C. Meunier, I. Segev. Playing the devil’s advocate: is the Hodgkin-Huxley model useful?. Trends Neurosci., 25 (2002), 558–563. [CrossRef] [PubMed] [Google Scholar]
- J. Modolo. Modélisation et analyse mathématique des effets de la stimulation cérébrale profonde dans la maladie de Parkinson. Thêse 2008. [Google Scholar]
- J. Modolo, A. Garenne, J. Henry, A. Beuter. Development and validation of a neural population model based on the dynamics of discontinuous membrane potential neuron model. J. Integr. Neurosci., 6 (2007), No. 4, 625–656. [CrossRef] [PubMed] [Google Scholar]
- J. Modolo, J. HenryA. Beuter. Dynamics of the subthalamo-pallidal complex in Parkinson’s Disease during deep brain stimulation. J. Biol. Phys., 34 (2008), 351–366. [Google Scholar]
- J. Modolo, E. Mosekilde, A. Beuter, New insights offered by a computational model of deep brain stimulation. J. Physiol. Paris, 101 (2007), 56–63. [CrossRef] [PubMed] [Google Scholar]
- D. Serre. Systemes de lois the conservation I. Hyperbolicité, entropies, ondes de choc. Diederot Editeur, Paris, 1996. [Google Scholar]
- J.H. Sheeba, A. Stefanovska, P.V. McClintock. Neuronal synchrony during anesthesia: a thalamocortical model. Biophys. J., 95 (2008), 2722–2727. [CrossRef] [PubMed] [Google Scholar]
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