Abstract
A recently developed continuous neuronal model is transformed into a system which is closely related to the theory of cellular control processes. In a broad region of parameter values periodic solutions of the equations describing the neuron do exist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen, C.F., Baumgarten, R. von, Takeda, R.: Pacemaker properties of completely isolated neurons in Aplysia california. Nature (Lond.) New Biol.233, 27–29 (1971)
Gainer, H.: Electrophysiological behavior of an endogenously active neurosecretory cell. Brain Res.39, 403–418 (1972)
Goodwin, B.C.: In: Weber, G. (Ed.): Advances in enzyme regulation. Vol. 3, p. 425. Oxford: Pergamon Press 1965
Griffith, J.S.: Mathematics of cellular control processes, I. Negative feedback to one gene. J. theor. Biol.20, 202–208 (1968)
Stein, R.B., Leung, K.V., Mangeron, D., Oĝuztöreli, M.N.: Improved neuronal models for studying neural networks. Kybernetik15, 1–9 (1974)
Tyson, J.J.: On the existence of oscillatory solutions in negative feedback cellular control processes. J. Math. Biol.1, 311–315 (1975)
Willems, J.L.: Stability theory of dynamical systems. London: Thomas Nelson Ltd. 1970
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
an der Heiden, U. Existence of periodic solutions of a nerve equation. Biol. Cybernetics 21, 37–39 (1976). https://doi.org/10.1007/BF00326671
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00326671