Dynamics of neuronal populations: The equilibrium solution

SIAM Journal on Applied Mathematics

Volumn 60, Issue 6, 2000, Pages 2009-2028

  Sirovich, L ^a,b   Omurtag, A ^a   Knight, B W ^a,b  

^a MOUNT SINAI SCHOOL OF MEDICINE   (United States)

^b ROCKEFELLER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; PHYSIOLOGICAL MODELS; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING;

NEURONS; SYNAPTIC DYNAMICS;

NEUROPHYSIOLOGY;

EID: 0034479938     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139998344921     Document Type: Article

References (22)

1. L. ABBOTT AND C. VAN VREESWIJK, Asynchronous states in networks of pulse-coupled oscillators, Phys. Rev. E, 48 (1993), pp. 1483-1490.
2. M. ABELES, Corticonics: Neural Circuits of the Cerebral Cortex, Cambridge University Press, Cambridge, UK, 1991.
3. T. CHAWANYA, T. AOYAGI, I. NISHIKAWA, K. OKUDA, AND Y. KURAMOTO, A model for feature linking via collective oscillations in the primary visual cortex, Biological Cybernetics, 68 (1993), pp. 483-490.
4. M.-N. CHEE-ORTS, K. PURPURA, AND L. OPTICAN, A Dynamical Model of the Primate's Early Visual Pathway: Effect of Luminance Contrast, Spatial Scale, and Spatial Orientation in Shaping Neuronal Firing Patterns, unpublished report, 1996.
5. W. GERSTNER, Time structure of the activity in neural network models, Phys. Rev. E, 51 (1995), pp. 738-758.
6. P. JOHANNESMA, Stochastic Neural Activity: A Theoretical Investigation, Ph.D. thesis, University of Nijmegen, Nijmegen, The Netherlands, 1969.
7. B. KNIGHT, Dynamics of encoding in a population of neurons, J. Gen. Physiol., 59 (1972a), pp. 734-766.
8. B. KNIGHT, Dynamics of encoding in neuron populations: Some general mathematical features, Neural Computation, 12 (2000), pp. 473-518.
9. B. KNIGHT, D. MANIN, AND L. SIROVICH, Dynamical models of interacting neuron populations, in Symposium on Robotics and Cybernetics: Computational Engineering in Systems Applications, E.C. Gerf, ed., Cite Scientifique, Lille, France, 1996.
10. C. KOCH AND I. SEGEV, Methods m Neuronal Modeling: from Synapses to Networks, MIT Press, Cambridge, MA, 1989.
11. M. MACKEY AND L. GLASS, Oscillation and chaos in physiological control systems, Science, 197 (1977), pp. 287-289.
12. T. MCKENNA, J. DAVIS, AND S. ZORNETZER, Single Neuron Computation, Academic Press, San Diego, CA, 1992.
13. E. MIROLLO AND S. STROGATZ, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), pp. 1645-1662.
14. A. OMURTAG, B. KNIGHT, AND L. SIROVICH, On the simulation of large populations of neurons, J. Comp. Neurosci., 8 (2000), pp. 51-63.
15. C. PESKIN, Mathematical Aspects of Heart Physiology, Lecture Notes, Courant Institute of Mathematical Sciences, New York University. New York, 1975.
16. L. SIROVICH, B. KNIGHT, AND A. OMURTAG, Dynamics of Neuronal Populations: The Stability of Equilibria, submitted.
17. D. SOMERS, S. NELSON, AND M. SUR, An emergent model of orientation selectivity in cat visual cortex simple cells, J. Neurosci., 15 (1995), pp. 5448-5465.
18. R. STEIN, A theoretical analysis of neuronal variability, Biophys. J., 5 (1965), pp. 173-194.
19. H. C. TUCKWELL, Introduction to Theoretical Neurobiology, Vol. 2, Cambridge University Press, Cambridge, UK, 1988.
20. C. VAN VREESWIJK AND L. ABBOTT. Self-sustained firing in populations of integrate-and-fire neurons, SIAM J. Appl. Math., 53 (1993), pp. 253-264.
21. W. WILBUR AND J. RINZEL, An analysis of Stein's model for stochastic neuronal excitation, Biological Cybernetics, 45 (1982), pp. 107-114.
22. F. WORGOTTER AND C. KOCH, A detailed model of the primary visual pathway in the cat: Comparision of afferent excitatory and intracortical inhibitory connection schemes for orientation selectivity, J. Neurosci., 11 (1991), pp. 1959-1979.