Pulse sequences generated by a degenerate analog neuron model
Tóm tắt
The response characteristics of an electronic neuron model proposed by the authors are investigated. Periodic stimulating pulse sequences with a fixed frequency are applied to the analog neuron model and the response pulse sequences are studied. In the degenerate case, the state transition of the neuron model during one period of the stimulating pulse sequence is described by a first order piecewise linear difference equation with a jump. It is shown that the periodic response pulse sequences of the neuron model belong to a special class of pulse sequences generated by a simple algorithm, and that the relation between the pulse width (or amplitude) of the stimulating pulse and the firing rate of the neuron model takes the form of an extended Cantor function.
Tài liệu tham khảo
Caianiello, E.R.: Outline of a theory of thought-processes and thinking machines. J. Theor. Biol. 1, 204–235 (1961)
Caianiello, E.R., DeLuca, A.: Decision equation for binary systems. Application to neuronal behavior. Kybernetik 3, 33–40 (1966)
Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers. Oxford: Clarendon Press 1961
Harmon, L.D.: Studies with artificial neurons. I. Properties and functions of an artificial neuron. Kybernetik 1, 89–101 (1961)
Hata, M.: Dynamics of Caianiello's equation. Preprint (1980)
Ikeda, N., Tsuruta, H., Sato, T.: Difference equation model of the entrainment of myocardial pacemaker cells based on the phase response curve. Biol. Cybern. 42, 117–128 (1981)
Keener, J.P.: Chaotic behavior in piecewise continuous difference equations. Trans. Am. Math. Soc. 261, 589–604 (1980)
McKean, H.P., Jr.: Nagumo's equation. Adv. Math. 4, 209–223 (1970)
Nagumo, J., Arimoto, S., Yoshizawa, S.: An active pulse transmission line simulating nerve axon. Proc. Inst. Radio Eng. 50, 2061–2070 (1962)
Nagumo, J., Sato, S.: On a response characteristic of a mathematical neuron model. Kybernetik 10, 155–164 (1972)
Rinzel, J., Keller, J.B.: Traveling nerve solutions of a nerve conduction equation. Biophys. J. 13, 1313–1336 (1973)
Sato, S.: Mathematical properties of responses of a neuron model. Kybernetik 11, 208–216 (1972)
Yoshizawa, S., Nagumo, J., Osada, H.: A Cantor function-like response characteristic of a neuron model. J. Faculty Eng., Univ. of Tokyo B 36, 59–90 (1981)