Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops
Mathematical Modelling of Natural Phenomena (2010)
- Volume: 5, Issue: 2, page 67-99
- ISSN: 0973-5348
Access Full Article
topAbstract
topHow to cite
topReferences
top- C. A. Bares, M. S. Suster, J. Shen B. L. McNaughton. Multistability of cognitive maps in the hippocampus of old rats. Nature, 388, 272-275 (1997).
- 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).
- R. M. Borisyuk A. Kirillov. Bifurcation analysis of a neural network model. Biological Cybernetics, 66319-325 (1992).
- C. Canavier, D. Baxter, J. Clark J. Byrne. Multiple modes of activity in a neuron model suggest a novel mechanism for the effects of neuromodulators. J. Neurophysiol., 72, 872-882 (1994).
- C. C. Chow, J. A. White, J. Ritt N. Kopell. Frequency control in synchronized networks of inhibitory neurons. Neural Comput., 5, 407-420 (1998).
- D. Cotreras, A. Destexhe, T. J. Sejnowski M. Steraide. Control of spatiotemporal coherence of a thalamic oscillation by corticothalamic feedback. Science, 274, 771-774 (1996).
- G. B. Ermentrout N. Kopell. Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc. Nat. Acad. Sci., 95, 1259-1264 (1998).
- J. Foss, A. Longtin, B. Mensour J. Milton. Multistability and delayed recurrent loops. Phys. Rev. Lett., 76, 708-711 (1996).
- J. Foss, F. Moss J. Milton. Noise, multistability, and delayed recurrent loops. Phys. Rev. E55, 4536-4543 (1997).
- J. Foss, J. Milton. Multistability in recurrent neural loops arising from delay. J. Neurophysiol., 84(2) 975-985 (2000).
- M. J. Gutnick D. A. Prince. Thalamocortical relay neurons: antidromic invasion of spikes from a cortical epileptogenic focus. Science, 176, 424-426 (1972).
- A. C. Guyton. Textbook of medical physiology. Saunders, Toronto, 1976.
- J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci., 79, 2554-2558 (1982).
- 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).
- N. Kopell, G. B. Ermentrout, M. A. Whittington R. D. Traub. Gamma rhythms and beta rhythms have different synchronization properties. PNAS, 97, 1867-1872 (2000).
- N. Kopell, D. Pervouchine, H. G. Rotstein, T. Netoff, M. Whittington, T. Gloveli. Multiple rhythms and switches in the nervous system. In press.
- J. Ma J. Wu. Multistability in spiking neuron models of delayed recurrent neural loops. Neural Comput., 19, 2124-2148 (2007).
- 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..
- 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.
- 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.
- 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).
- M. Morita. Associative memory with non-monotone dynamics. Neural Networks, 6, 115-123 (1993).
- 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).
- 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).
- P. Tiňo, B. G. Horne C. 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).
- R.D. Traub, R. Miles. Neuronal networks of the hippocampus. Cambridge University Press, New York, 1991.