Biological Cybernetics

, Volume 52, Issue 6, pp 367–376 | Cite as

Sustained oscillations generated by mutually inhibiting neurons with adaptation

  • Kiyotoshi Matsuoka


Autonomic oscillatory activities exist in almost every living thing and most of them are produced by rhythmic activities of the corresponding neural systems (locomotion, respiration, heart beat, etc.). This paper mathematically discusses sustained oscillations generated by mutual inhibition of the neurons which are represented by a continuous-variable model with a kind of fatigue or adaptation effect. If the neural network has no stable stationary state for constant input stimuli, it will generate and sustain some oscillation for any initial state and for any disturbance. Some sufficient conditions for that are given to three types of neural networks: lateral inhibition networks of linearly arrayed neurons, symmetric inhibition networks and cyclic inhibition networks. The result suggests that the adaptation of the neurons plays a very important role for the appearance of the oscillations. Some computer simulations of rhythic activities are also presented for cyclic inhibition networks consisting of a few neurons.


Fatigue Neural Network Respiration Computer Simulation Stationary State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Barlow RB Jr, Fraioli A (1978) Inhibition in the Limulus lateral eye in situ. Gen Physiol 71:699–720Google Scholar
  2. Friesen WO, Stent GS (1977) Generation of a locomotory rhythm by a neural network with recurrent cyclic inhibition. Biol Cybern 28:27–40Google Scholar
  3. Hadeler KP (1974) On the theory of lateral inhibition. Kybernetik 14:161–165Google Scholar
  4. Harmon LD, Lewis ER (1966) Neural modeling. Physiol Rev 46:513–591Google Scholar
  5. Kling U, Székely G (1968) Simulation of rhythmic nervous activities. I. Function of networks with cyclic inhibitions. Kybernetik 5:89–103Google Scholar
  6. Luciano DS, Vander AJ, Sherman JH (1978) Human functions and structure. McGraw-Hill, London, New York, pp 105–106Google Scholar
  7. Marden M (1966) Geometry of polynomials. American Mathematical Society, Providence, Rhode Island, pp 166–193Google Scholar
  8. Matsuoka K (1984) The dynamic model of binocular rivalry. Biol Cybern 49:201–208Google Scholar
  9. Morishita I, Yajima A (1972) Analysis and simulation of networks of mutually inhibiting neurons. Kybernetik 11:154–165Google Scholar
  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)Google Scholar
  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 171–194Google Scholar
  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)Google Scholar
  13. Suzuki R, Katsuno I, Matano K (1971) Dynamics of “Neuron Ring”. Kybernetik 8:39–45Google Scholar
  14. Wall C III, Kozak WM, Sanderson AC (1979) Entrainment of oscillatory neural activity in the cat's lateral nucleus. Biol Cybern 33:63–75Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Kiyotoshi Matsuoka
    • 1
  1. 1.Department of Control EngineeringKyushu Institute of TechnologyTobata, KitakyushuJapan

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