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A theory of oscillatory instability in two-state systems in relation to nerve excitation

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Abstract

The oscillatory aspect in a system having two steady states is studied theoretically using a model of excitable nerve membrane. The condition for the occurrence of oscillatory instability is discussed on the basis of the kinetic picture of nerve excitation in consideration of the non-Markoffian effect caused by ion transport in the system. Small oscillations around a steady state as well as a giant fluctuation between two states are obtained. Results are compared with experiments carried out with squid giant axons perfused intracellularly.

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Authors and Affiliations

  1. Faculty of Pharmaceutical Sciences, Hokkaido University, Sapporo, Japan

    Yöji Aizawa & Yonosuke Kobatake

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  1. Yöji Aizawa
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  2. Yonosuke Kobatake
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Aizawa, Y., Kobatake, Y. A theory of oscillatory instability in two-state systems in relation to nerve excitation. Bltn Mathcal Biology 38, 351–358 (1976). https://doi.org/10.1007/BF02462210

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  • DOI: https://doi.org/10.1007/BF02462210

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