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

For citation:

Ezhov D. M., Kurbako A. V., Ponomarenko V. I., Prokhorov M. D. Modified FitzHugh-Nagumo oscillator with spiking activity dependent on the duration of external impulse action. Izvestiya VUZ. Applied Nonlinear Dynamics, 2025, vol. 33, iss. 6, pp. 917-928. DOI: 10.18500/0869-6632-003193, EDN: IJPPGU

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Language: 
Russian
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Article
UDC: 
537.86
DOI: 
10.18500/0869-6632-003193
EDN: 
IJPPGU

Modified FitzHugh-Nagumo oscillator with spiking activity dependent on the duration of external impulse action

Autors: 
Ezhov Dmitrii Maximovich, Saratov State University
Kurbako Aleksandr Vasilievich, Saratov State University
Ponomarenko Vladimir Ivanovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The purpose of the study is to develop and investigate a modified FitzHugh-Nagumo oscillator, the spiking activity of which is determined not only by the amplitude, but also by the duration of the external impulse signal applied to the input of the oscillator.

Methods. We have added an equation to the system of known equations describing the dynamics of the FitzHugh-Nagumo oscillator with a constant threshold parameter value. This additional equation describes the change in the threshold parameter over time under the influence of external impulse signals. For various values of the parameters of external impulses, a numerical study of the dynamics of the proposed oscillator, which is in a state of equilibrium in the absence of external influence, is carried out.

Results. It is shown that, unlike the classical FitzHugh-Nagumo oscillator, the modified oscillator is capable of demonstrating a sequence of several spikes in response to a single external impulse action, and the oscillator dynamics depends on both the amplitude and the duration of external impulses. In addition, the proposed oscillator can be excited by a sequence of impulses with an amplitude below the threshold.

Conclusion. The proposed modified FitzHughNagumo oscillator can be used to construct spiking neural networks. Learning of such networks can be implemented by changing synaptic connections by adjusting the synapse weights corresponding to the duration of external
impulse signals. The proposed modification of the FitzHugh-Nagumo oscillator can be implemented quite simply in a radio physical experiment using analog electronic elements and digital circuits regulating the duration of input impulses.
 

Key words: 
neuron-like oscillator
FitzHugh-Nagumo model
synaptic connection
impulse action
Acknowledgments: 
This study was supported by the Russian Science Foundation, Grant No. 23-12-00103, https://rscf.ru/project/23-12-00103/
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Received: 
03.06.2025
Accepted: 
02.09.2025
Available online: 
12.09.2025
Published: 
28.11.2025
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