Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 2, 2010
Mathematics and neuroscience
Page(s) 67 - 99
DOI https://doi.org/10.1051/mmnp/20105203
Published online 10 March 2010
  1. C. A. Bares, M. S. Suster, J. ShenB. L. McNaughton. Multistability of cognitive maps in the hippocampus of old rats. Nature, 388, 272-275 (1997). [CrossRef] [PubMed]
  2. A. Beuter, J. G. Milton, C. Labrie, L. Glass. Complex motor dynamics and control in multi-loop negative feedback systems. Proc IEEE Systems Man Cybern. 899-902. (1989). [CrossRef]
  3. R. M. BorisyukA. Kirillov. Bifurcation analysis of a neural network model. Biological Cybernetics, 66 319-325 (1992). [CrossRef] [PubMed]
  4. C. Canavier, D. Baxter, J. ClarkJ. Byrne. Multiple modes of activity in a neuron model suggest a novel mechanism for the effects of neuromodulators. J. Neurophysiol., 72, 872-882 (1994). [PubMed]
  5. C. C. Chow, J. A. White, J. RittN. Kopell. Frequency control in synchronized networks of inhibitory neurons. Neural Comput., 5, 407-420 (1998).
  6. D. Cotreras, A. Destexhe, T. J. SejnowskiM. Steraide. Control of spatiotemporal coherence of a thalamic oscillation by corticothalamic feedback. Science, 274, 771-774 (1996). [CrossRef] [PubMed]
  7. G. B. ErmentroutN. Kopell. Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc. Nat. Acad. Sci., 95, 1259-1264 (1998). [CrossRef]
  8. J. Foss, A. Longtin, B. MensourJ. Milton. Multistability and delayed recurrent loops. Phys. Rev. Lett., 76, 708-711 (1996). [CrossRef] [PubMed]
  9. J. Foss, F. MossJ. Milton. Noise, multistability, and delayed recurrent loops. Phys. Rev. E 55, 4536-4543 (1997). [CrossRef]
  10. J. Foss, J. Milton. Multistability in recurrent neural loops arising from delay. J. Neurophysiol., 84(2) 975-985 (2000). [PubMed]
  11. M. J. GutnickD. A. Prince. Thalamocortical relay neurons: antidromic invasion of spikes from a cortical epileptogenic focus. Science, 176, 424-426 (1972). [CrossRef] [PubMed]
  12. A. C. Guyton. Textbook of medical physiology. Saunders, Toronto, 1976.
  13. J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci., 79, 2554-2558 (1982). [NASA ADS] [CrossRef]
  14. J. J. Hopfield. Neurons with grades response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci., 81, 3088-3092 (1984). [CrossRef]
  15. N. Kopell, G. B. Ermentrout, M. A. WhittingtonR. D. Traub. Gamma rhythms and beta rhythms have different synchronization properties. PNAS, 97, 1867-1872 (2000). [CrossRef]
  16. N. Kopell, D. Pervouchine, H. G. Rotstein, T. Netoff, M. Whittington, T. Gloveli. Multiple rhythms and switches in the nervous system. In press.
  17. J. MaJ. Wu. Multistability in spiking neuron models of delayed recurrent neural loops. Neural Comput., 19, 2124-2148 (2007). [CrossRef] [MathSciNet] [PubMed]
  18. J. Ma, J. Wu. Transition and coexistence of periodic patterns in spiking neuron models of delayed recurrent inhibitory loops. Submitted to SIAM J. Appl. Math..
  19. J. Milller. What is the contribution of axonal conduction delay to temporal structure in brain dynamics? 53–57. In: Oscillatory event-related brain dynamics. C. Pantev, Ed. Plenum, New York, 1994.
  20. J. Milton. Epilepsy: Multistability in a dynamic disease. In: Self-organized biological dynamics and nonlinear control. J. Walleczek, Ed. Cambridge University Press, Cambridge, 374-386, 2000.
  21. J. Milton. Insights into seizure propagation from axonal conduction times. In: Epilepsy as a dynamic disease. J. Milton, P. Jung, Eds. New York. Springer-Verlag 15-23 (2002).
  22. M. Morita. Associative memory with non-monotone dynamics. Neural Networks, 6, 115-123 (1993). [CrossRef]
  23. M. Proctor, K. Gale. Basal Ganglia and Brainstem Anatomy and Physiology, In: Epilepsy: A comprehensive textbook. J. Engel, T. A. Pedley, Eds. Philadelphia, PA: Lippincott-Raven 353-368 (1997).
  24. P. A. Schwartzkroin, D. C. McIntyre. Limbic anatomy and physiology. In: Epilepsy: a comprehensive textbook. J. Engel, T. A. Pedley, Eds. Philadelphia, PA: Lippincott-Raven 323-340 (1997).
  25. P. Tiňo, B. G. HorneC. L. Giles. Attractive periodic sets in discrete-time recurrent networks with emphasis on fixed-point stability and bifurcations in two-neuron networks. Neural Comput., 13, 1379-1414 (2001). [CrossRef] [PubMed]
  26. R.D. Traub, R. Miles. Neuronal networks of the hippocampus. Cambridge University Press, New York, 1991.

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