[Identification of nonlinear models of biological membranes by the method of fixed voltage]

A mathematical substantiation of the method suggested by Hodkin and Huxley in 1952 for the identification of nonlinear systems is presented. A procedure for the application of this method was developed, which involves creating the structure of a mathematical model, carrying out a series of tests with specially chosen signals, and finding the unknown parameters. The basic requirements to admissible sets of entrance and target signals and the operator of the system were determined. It was shown that it should be quite continuous, the minimal number of unknown parameters and the minimal complexity of structure of the operator should provide the required quality of approximation. The merits and demerits of the mathematical models of Hodkin-Huxley and Noble, and the procedures used for their creation are discussed. The structure of the operator for the identification of mathematical models of excitable membranes when a large number of membrane currents is considered is offered. It was found that nonlinear electric properties of biological membranes can be identified using tests with other kinds of "fixed" parameters, for example, the method of "fixed" current, the fixed linearly increasing voltage, and others.