Root / CYBERNETICS AND PHYSICS / Volume 15, 2026, Number 1 / Identification of generalized van der Pol equations from experimental time series of electronic neuron

Identification of generalized van der Pol equations from experimental time series of electronic neuron

Lev Takaishvili, Vladimir Ponomarenko, Ilya V. Sysoev

Currently, new electronic generators of neuron-like activity are being developed, which can be used both to build spike neural networks and, in the longer term, to solve the problems of neuroprosthetics and creation of artificial life. At the same time, the mathematical description of such artificial neurons is usually qualitative or fragmentary. Though writing equations from the first principles (e. g. from the Kirchhoff’s laws) is still the main tool, there is another useful approach — system identification (model reconstruction) from experimental series. Actually, a combination of both approaches can give even more than each of them separately. The purpose of this work is to provide a new specific approach for identification of models which can to some extent be described by a generalized van der Pol oscillator. Since we propose this approach for a specific experimental device (electronic neuron) and test using its time series, we focused on some practical factors. First, we abandoned theoretical formulae for dissipation and potential functions and reconstructed them in the most general form without any additional assumptions. Second, we switched to equations integrated in time to reduce the impact of the measurement noise. Then, we considered the possibility of hysteresis for the dissipation function. Finally, we tested the approach based on series from three different instances of the same generator. We showed that the proposed approach can be useful to obtain the equations of the setup which really match the observed data.
CYBERNETICS AND PHYSICS, VOL. 15, NO. 1, 2026, 93–99
https://doi.org/10.35470/2226-4116-2026-15-1-93-99

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