https://doi.org/10.1140/epjb/s10051-026-01125-2
Research - Statistical and Nonlinear Physics
Resonance phenomenon for a memristive Hindmarsh–Rose neuronal model with multiplicative and additive noise
1
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, 611731, Chengdu, China
2
AVIC Chengdu Aircraft Industrial (Group) Co., Ltd, 610091, Chengdu, China
3
School of Information and Control Engineering, Southwest University of Science and Technology, 621010, Mianyang, China
a
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Received:
18
July
2025
Accepted:
13
January
2026
Published online:
3
March
2026
Abstract
The stochastic resonance (SR) phenomenon for a memristive three-dimensional Hindmarsh–Rose (HR) neuronal model with multiplicative and additive white noise driven by weak periodic force and stochastic telegraph signal is investigated. The three-dimensional HR model is transformed into a one-dimensional Langevin equation applying equilibrium point method. Based on adiabatic approximation condition and two-state theory, the system output signal-to-noise ratio (SNR) is deduced. The result shows that memristor coupling strength of the HR model can induce two peaks as the SNR changes with the coupling strength. Double SR appears when the SNR varies with the intensities of the multiplicative and additive noise. One resonance peak takes place as the SNR varies with the amplitude of the stochastic telegraph signal. The non-monotonous dependence of the SNR on system parameter is discussed.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
