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运动协调模型中基于神经学的耦合函数

Neurologically Motivated Coupling Functions in Models of Motor Coordination.

作者信息

Słowiński Piotr, Al-Ramadhani Sohaib, Tsaneva-Atanasova Krasimira

机构信息

Department of Mathematics and the Living Systems Institute, Translational Research Exchange @Exeter, University of Exeter, Exeter EX4 4QD, UK (http://emps.exeter.ac.uk/mathematics/staff/pms210).

Department of Mathematics, College of Education for Pure Science, University of Mosul, Mosul, 41002, Iraq.

出版信息

SIAM J Appl Dyn Syst. 2020;19(1):208-232. doi: 10.1137/19M1279381. Epub 2020 Jan 14.

DOI:10.1137/19M1279381
PMID:31992962
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC6986925/
Abstract

We present an analysis of two Haken-Kelso-Bunz (HKB) oscillators coupled by a neurologically motivated function. We study the effect of time delay and weighted self-feedback and mutual feedback on the synchronization behavior of the model. We focus on identifying parameter regimes supporting experimentally observed decrease in oscillation amplitude and loss of anti-phase stability that has inspired the development of the HKB model. We show that a combination of cross-talk and nonlinearity in the coupling, along with physiologically relevant time delay, is able to quantitatively account for both drop in oscillation amplitude and loss of anti-phase stability in a frequency dependent manner. Furthermore, we demonstrate that the transition between discrete and rhythmic movements could be captured by this model. To this end, we carry out theoretical and numerical analysis of the emergence of in-phase and anti-phase oscillations.

摘要

我们对两个由具有神经学动机的函数耦合的哈肯 - 凯尔索 - 布恩兹（HKB）振荡器进行了分析。我们研究了时间延迟以及加权自反馈和互反馈对该模型同步行为的影响。我们专注于确定支持实验观察到的振荡幅度减小和反相稳定性丧失的参数范围，这激发了HKB模型的发展。我们表明，耦合中的串扰和非线性的组合，以及生理相关的时间延迟，能够以频率依赖的方式定量解释振荡幅度的下降和反相稳定性的丧失。此外，我们证明该模型可以捕捉离散运动和节律性运动之间的转变。为此，我们对同相和反相振荡的出现进行了理论和数值分析。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/ea3e/6986925/ee9a7adbc0ee/EMS85471-f011.jpg
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