Objective. Fractional calculus plays a key role in the analysis of neural dynamics. In particular, fractional calculus has been recently exploited for analyzing complex biological systems and capturing intrinsic phenomena. Also, artificial neural networks have been shown to have complex neuronal dynamics and characteristics that can be modeled by fractional calculus. Moreover, for a neural microcircuit placed on the spinal cord, fractional calculus can be employed to model the central pattern generator (CPG). However, the relation between the CPG and the motor cortex is still unclear. Approach. In this paper, fractional-order models of the CPG and the motor cortex are built on the Van der Pol oscillator and the neural mass model (NMM), respectively. A self-consistent mean field approximation is used to construct the potential landscape of the Van der Pol oscillator. This landscape provides a useful tool to observe the 3D dynamics of the oscillator. To infer the re...

中文翻译：

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运动皮层和中央模式发生器的分数阶模型的动力学和耦合。

客观的。分数阶微积分在神经动力学分析中起着关键作用。特别是，分数阶微积分最近被用于分析复杂的生物系统和捕捉内在现象。此外，人工神经网络已被证明具有复杂的神经元动力学和特征，可以通过分数微积分进行建模。此外，对于放置在脊髓上的神经微电路，可以使用分数计算来模拟中央模式发生器 (CPG)。然而，CPG 与运动皮层之间的关系仍不清楚。方法。在本文中，CPG 和运动皮层的分数阶模型分别建立在范德波尔振荡器和神经质量模型 (NMM) 上。自洽平均场近似用于构建范德波尔振荡器的潜在景观。该景观提供了一个有用的工具来观察振荡器的 3D 动态。为了推断出...