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Neurologically Motivated Coupling Functions in Models of Motor Coordination.
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-01-14 , DOI: 10.1137/19m1279381 Piotr Słowiński 1 , Sohaib Al-Ramadhani 2 , Krasimira Tsaneva-Atanasova 3
SIAM Journal on Applied Dynamical Systems ( IF 2.1 ) Pub Date : 2020-01-14 , DOI: 10.1137/19m1279381 Piotr Słowiński 1 , Sohaib Al-Ramadhani 2 , Krasimira Tsaneva-Atanasova 3
Affiliation
SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 1, Page 208-232, January 2020.
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.
中文翻译：
运动协调模型中的神经驱动耦合功能。
SIAM 应用动力系统杂志，第 19 卷，第 1 期，第 208-232 页，2020 年 1 月。
我们对两个由神经驱动函数耦合的 Haken--Kelso--Bunz (HKB) 振荡器进行了分析。我们研究了时间延迟和加权自反馈和互反馈对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损失的参数机制，这启发了 HKB 模型的开发。我们表明，耦合中的串扰和非线性以及生理相关的时间延迟的组合能够以频率相关的方式定量地解释振荡幅度的下降和反相稳定性的损失。此外，我们证明该模型可以捕获离散运动和有节奏运动之间的过渡。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。
更新日期：2020-01-14
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.
中文翻译：
运动协调模型中的神经驱动耦合功能。
SIAM 应用动力系统杂志，第 19 卷，第 1 期，第 208-232 页，2020 年 1 月。
我们对两个由神经驱动函数耦合的 Haken--Kelso--Bunz (HKB) 振荡器进行了分析。我们研究了时间延迟和加权自反馈和互反馈对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损失的参数机制，这启发了 HKB 模型的开发。我们表明，耦合中的串扰和非线性以及生理相关的时间延迟的组合能够以频率相关的方式定量地解释振荡幅度的下降和反相稳定性的损失。此外，我们证明该模型可以捕获离散运动和有节奏运动之间的过渡。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。
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