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Prog. Theor. Phys. Vol. 79 No. 5 (1988) pp. 1061-1068
Oscillatory and Excitable Behaviors in a Population of Model Neurons
Hidetsugu Sakaguchi
Department of Physics, Kyoto University, Kyoto 606
(Received December 2, 1987)
Abstract:
A population containing both excitatory and inhibitory neurons is studied with coupled differential equations proposed by Wilson and Cowan. The system exhibits stationary, oscillatory or excitable behavior as the coupling strength is changed. Bifurcation analyses and numerical calculations are carried out to investigate the transitions to the oscillatory and excitable states. In the latter a pulse solution is found numerically in a coupled one-dimensional system composed of the excitable populations.
URL :
http://ptp.ipap.jp/link?PTP/79/1061/
DOI : 10.1143/PTP.79.1061
References:
- G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977).
- A. Gierer and H. Meinhart, Kyben, 12 (1972), 30.
- H. R. Wilson and J. D. Cowan, Biophys. J. 12 (1972), 1.
- S. Amari, Proc. IEEE 59 (1971), 35.
S. Amari, IEEE Trans. SMC-2 (1972), 643.
- S. Amari, Kyben. 14 (1974), 215.
- R. Thom, Structural Stability and Morphogenesis (Benjamin, MA, 1975).
- G. B. Ermentrout and J. D. Cowan, SIAM J. Appl. Math. 38 (1980), 1.
- J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, Heidelberg, New York, 1984).
- H. R. Wilson and J. D. Cowan, Kyben. 13 (1973), 55.
- S. Amari, Biol. Cyben. 27 (1977), 77.
- G. B. Ermentrout, Lecture Notes in Biomath., ed. S. Amari and M. A. Arbib (Springer, 1982), p. 57.
