ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Susorov M. A., Sysoev I. V., Kornilov M. V. Frequency divider circuit as a chain of unidirectionally coupled generators of neuron-like activity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2026, vol. 34, iss. 4, pp. 603-613. DOI: 10.18500/0869-6632-003229, EDN: ITPZIM

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Language: 
Russian
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003229
EDN: 
ITPZIM

Frequency divider circuit as a chain of unidirectionally coupled generators of neuron-like activity

Autors: 
Susorov Maxim Anatolievich, Peter the Great St. Petersburg Polytechnic University
Sysoev Ilya Vyacheslavovich, Peter the Great St. Petersburg Polytechnic University
Kornilov Maksim Vyacheslavovich, Saratov State University
Abstract: 

The purpose is to investigate the possibility of a chain of unidirectionally coupled radio-frequency oscillators, constructed by means of circuit implementation of modified phase-locked loop equations with a nonlinear coupling function in the form of a hyperbolic tangent, operating as a cascade frequency divider.

Methods. In this work, the mathematical model of a chain of oscillators is numerically investigated for various coupling coefficients and numbers of elements, and the dependence of the frequency in the chain on the parameters of an individual oscillator and on the coupling parameters is studied. In order to realize forced oscillations, for all generators except the master one, the DC bias voltage parameter, which is responsible, among other things, for the oscillation frequency, is set as small as possible (with an assessment of the feasibility of
achieving such small values in a physical experiment). This allows, at large times, the regime of intrinsic dynamics to be considered as close to subthreshold excitable behavior.

Results. For a system of two oscillators (master–slave), it is shown that at a coupling amplitude of 1/2, a stable frequency-division-by-two regime is realized, which is structurally stable over a wide range of detunings of the DC bias parameter. Investigation of a cascade architecture containing up to seven slave generators revealed that for short chains (up to four stages long), the division occurs with efficiency close to ideal (each stage provides a twofold frequency reduction). However, as the number of cascades increases, the efficiency decreases: the frequency ratio of adjacent stages drops

Conclusion. The obtained results can be used in the design of analog frequency dividers and are useful for modeling the generation of low-frequency rhythms in the brain by converting higher-frequency ones.
 

Key words: 
modified electronic neuron
cascade frequency divider
neuromorphic systems
synaptic coupling
Acknowledgments: 
The research was supported by the Russian Science Foundation grant No. 25-22-00406, https://rscf.ru/project/25-22-00406/.
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Received: 
03.07.2026
Accepted: 
14.07.2026
Available online: 
15.07.2026
Published: 
31.07.2026
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