https://doi.org/10.1140/epjp/s13360-024-05059-5
Regular Article
Noise-induced extreme events in integer and fractional-order memristive Hindmarsh–Rose neuron models: a comprehensive study
Department of Physics, Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, 613 401, Thanjavur, India
Received:
29
January
2024
Accepted:
4
March
2024
Published online:
26
March
2024
The investigation centers on the memristive Hindmarsh–Rose (HR) neuron model subjected to white Gaussian noise. This study explores the occurrence of extreme events (EE)—sudden, infrequent, and high-amplitude spikes induced by noise within the system. We specifically examine the probability density function (PDF) of inter-spike intervals (ISI) across different noise intensities to gauge the impact. Our findings reveal a notable P-bifurcation with increasing noise intensity, indicating a shift in the number of modes within the PDF and a transition from bounded to irregular spikes of different amplitudes. Consequently, there is a discernible rise in the probability of longer ISI, primarily attributable to the emergence of EE. Furthermore, we have employed the vector field approach to estimate the system’s energy function, revealing an elevation in the average energy during the emergence of EE. This investigation extends to a fractional order model for further exploring the role of noise and the order of integration in inducing EE. Given the susceptibility of neurons to real-world noise, the insights garnered from this study contribute to a better understanding of the influence of noise on biological oscillatory systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
