Department of Engineering Mathematics, University of Bristol, Bristol, BS8 1UB, UK.
Biol Cybern. 2021 Aug;115(4):343-364. doi: 10.1007/s00422-021-00879-5. Epub 2021 Jun 5.
The widely cited Haken-Kelso-Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.
广泛引用的运动协调的哈肯-凯尔索-邦茨（HKB）模型在大量应用中得到了应用。在本文中，我们通过分析表明，两个振荡器的弱阻尼、弱耦合 HKB 模型仅取决于两个无量纲参数；线性阻尼系数与线性耦合系数之比，以及组合非线性阻尼系数与组合非线性耦合系数之比。我们用一个力学模拟来说明我们的结果。我们利用我们的分析结果来预测任意参数区域的行为，并展示这如何帮助我们解释和扩展全 HKB 模型的最新数值延拓结果。关键的发现是，HKB 模型在生物相关的参数区域中包含了大量尚未在实验或数值模拟中观察到的行为。这一观察结果对虚拟伙伴交互和人类动态钳的发展具有重要意义，并且可能对 HKB 模型本身也具有重要意义。
