https://doi.org/10.1140/epjb/s10051-024-00751-y
Regular Article - Statistical and Nonlinear Physics
Effects of external stimuli on the dynamics of deterministic and stochastic Hindmarsh–Rose neuron models
Departamento de Física, Universidade do Estado de Santa Catarina, UDESC, Joinville 89219-710, SC, Brazil
Received:
7
February
2024
Accepted:
15
July
2024
Published online:
5
August
2024
We investigate the nonlinear dynamics of the deterministic and stochastic Hindmarsh–Rose (HR) neuron models under the influence of an external sinusoidal electric current and magnetic flow effects. In the deterministic regime, in the absence of a magnetic field, we observe multistability between periodic and chaotic attractors. This is accompanied by the emergence of self-similar windows of chaotic dynamics that converge within a broad domain of periodic dynamics in parameter space. Introducing a magnetic flux partially suppresses chaotic dynamics while maintaining multistability. Under stochastic conditions due to the introduction of Gaussian noise with arbitrarily small intensity, D, noise triggers transitions between coexisting states, exhibiting a preference for specific attractors from the deterministic case without returning to any other coexisting metastable states. By increasing D and appropriately adjusting the remaining control parameters of the HR neuron model, it becomes feasible to achieve regimes of noise-induced chaos or noise-induced stabilization, effectively suppressing chaotic dynamics. Furthermore, within this framework, we explore the existence of transient chaotic dynamics.
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© The Author(s), under exclusive licence to EDP Sciences, SIF 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.
