The dynamics of cortical neuronal activity plays important roles in controlling body movement and is regulated by connection weights between neurons in a cortex-basal ganglia-thalamus (BGCT) loop. Beta-band oscillation of cortical activity is closely associated with the movement disorder of Parkinson's disease, which is caused by an imbalance in the connection weights of direct and indirect pathways in the BGCT loop. In this study, the authors investigate how the dynamics of cortical activity are modulated by connection weights of direct and indirect pathways in the BGCT loop under low dopamine levels through bifurcation analyses and potential landscapes. The results reveal that cortical activity displays rich dynamics under different connection weights, including one, two, or three stable steady states, one or two stable limit cycles, and the coexistence of one stable limit cycle with one stable steady state or two stable ones. For a low dopamine level, cortical activity exhibits oscillation for larger connection weights of direct and indirect pathways. The stability of these stable dynamics is explored by the potential landscapes.

中文翻译：

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皮质-基底神经节-丘脑模型的分叉分析和潜在景观。

皮质神经元活动的动力学在控制人体运动中起着重要作用，并受皮质-基底神经节-丘脑（BGCT）回路中神经元之间的连接权重的调节。皮层活动的β波段振荡与帕金森氏病的运动障碍密切相关，帕金森氏病的运动障碍是由BGCT回路中直接和间接途径的连接权重不平衡引起的。在这项研究中，作者通过分叉分析和潜在景观研究了在低多巴胺水平下，BGCT环路中直接和间接途径的连接权重如何调节皮层活动的动力学。结果表明，在不同的连接权重下，皮质活动显示出丰富的动力学，包括一个，两个或三个稳定的稳态，一个或两个稳定的极限循环，一个稳定的极限环与一个稳定的或两个稳定的极限并存。对于低的多巴胺水平，对于直接和间接途径的较大连接权重，皮质活性表现出振荡。这些稳定动力的稳定性由潜在景观来探索。