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Asymmetry of synchronisation tongue in persistent sodium plus potassium neuron model
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Khovanov, I. A., Perry, S. and Khovanova, N. A. (2022) Asymmetry of synchronisation tongue in persistent sodium plus potassium neuron model. Communications in Nonlinear Science and Numerical Simulation, 105 . 106071. doi:10.1016/j.cnsns.2021.106071 ISSN 1007-5704.
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WRAP-asymmetry-synchronisation-tongue-persistent-sodium-plus-potassium-neuron-model-Khovanov-2021.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (5Mb) | Preview |
Official URL: https://doi.org/10.1016/j.cnsns.2021.106071
Abstract
In recent experimental studies, cardio-respiratory synchronisation was observed when the respiration rate was higher than the resting heart rate. Under this condition, there is a strong asymmetry in the synchronisation tongue towards frequencies higher than that of an unperturbed self-oscillator. These experimental results are compelling because they support a novel hypothesis about the interaction of cardiac and respiratory centres in the brain. This hypothesis, however, required further validation; we aimed to observe the key experimental features in related dynamical models. A number of simple self-oscillatory systems under an external driving force have been considered in this work, and a persistent sodium plus potassium neuron model was found to display the strong asymmetry, which is the key feature of the experimental observations. Bifurcations and other changes in the model’s state space were considered by varying the amplitude and frequency of the external force. It was shown that the strong asymmetry in the synchronisation tongue is linked to a non-uniformity of the surface of the non-synchronous invariant torus, and, within a certain range of parameters, to the additional saddle–node bifurcations of cycles. Then, it was demonstrated that the torus non-uniformity leads to changes in the shape of the phase difference potential as the amplitude increases. To illustrate the latter effect, a numerical approach for estimating the one dimensional phase difference profile and providing the corresponding explicit analytical expression is developed. Also, a discrepancy in synchronisation boundaries obtained by two different approaches, one based on bifurcational analysis and the other on a time series technique, was observed. The latter observation stresses the necessity of considering the standard deviation of instantaneous frequency alongside the mean value for the non-ambiguous identification of synchronisation in periodically driven systems.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QP Physiology |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Synchronization , Respiration -- Regulation , Respiration -- Simulation methods, Neurons, Bifurcation theory | ||||||||
| Journal or Publication Title: | Communications in Nonlinear Science and Numerical Simulation | ||||||||
| Publisher: | Elsevier Science BV | ||||||||
| ISSN: | 1007-5704 | ||||||||
| Official Date: | February 2022 | ||||||||
| Dates: |
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| Volume: | 105 | ||||||||
| Article Number: | 106071 | ||||||||
| DOI: | 10.1016/j.cnsns.2021.106071 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 12 November 2021 | ||||||||
| Date of first compliant Open Access: | 19 October 2022 | ||||||||
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