Sustained oscillations generated by mutually inhibiting neurons with adaptation. (English) Zbl 0574.92013

The basic model of a neuron with adaptation is the following: \[ \tau \dot x+x=\sum^{n}_{j=1}C_ js_ j-bz,\quad T\dot z+z=\max (0,x) \] where z represents the degree of adaptation. For three types of networks with inhibition is shown that sustained oscillations (not necessarilly periodic) may be generated for any initial state and any disturbance. The author stresses the significance of adaptation for the occurrence of this phenomenon. Computer simulations are presented.


92Cxx Physiological, cellular and medical topics
94C99 Circuits, networks
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[1] Barlow RB Jr, Fraioli A (1978) Inhibition in the Limulus lateral eye in situ. Gen Physiol 71:699-720
[2] Friesen WO, Stent GS (1977) Generation of a locomotory rhythm by a neural network with recurrent cyclic inhibition. Biol Cybern 28:27-40
[3] Hadeler KP (1974) On the theory of lateral inhibition. Kybernetik 14:161-165 · Zbl 0276.92014
[4] Harmon LD, Lewis ER (1966) Neural modeling. Physiol Rev 46:513-591
[5] Kling U, SzĂ©kely G (1968) Simulation of rhythmic nervous activities. I. Function of networks with cyclic inhibitions. Kybernetik 5:89-103 · Zbl 0164.50601
[6] Luciano DS, Vander AJ, Sherman JH (1978) Human functions and structure. McGraw-Hill, London, New York, pp 105-106
[7] Marden M (1966) Geometry of polynomials. American Mathematical Society, Providence, Rhode Island, pp 166-193
[8] Matsuoka K (1984) The dynamic model of binocular rivalry. Biol Cybern 49:201-208 · Zbl 0527.92028
[9] Morishita I, Yajima A (1972) Analysis and simulation of networks of mutually inhibiting neurons. Kybernetik 11:154-165 · Zbl 0241.92004
[10] Nagashino H, Tamura H, Ushita T (1981) Relations between initial conditions and periodic firing modes in reciprocal inhibition neural networks. Trans IECE Jpn J64-A: 378-385 (in Japanese)
[11] Reiss R (1962) A theory and simulation of rhythmic behavior due to reciprocal inhibition in nerve nets. Proc. of the 1962 A.F.I.P.S. Spring Joint Computer Conference. Vol. 21 National Press, pp 171-194
[12] Sugawara K, Harao M, Noguchi S (1983) On the stability of equilibrium states of analogue neural networks. Trans IECE Jpn J 66-A:258-265 (in Japanese)
[13] Suzuki R, Katsuno I, Matano K (1971) Dynamics of ?Neuron Ring?. Kybernetik 8:39-45
[14] Wall C III, Kozak WM, Sanderson AC (1979) Entrainment of oscillatory neural activity in the cat’s lateral nucleus. Biol Cybern 33:63-75
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