https://doi.org/10.1140/epjs/s11734-025-02090-0
Regular Article
Dynamic analyses on different frequency bands in a Parkinson’s disease model with time-delay
1
School of Mathematics and Statistics, Fujian Normal University, 350117, Fuzhou, China
2
FJKLMAA and Center for Applied Mathematics of Fujian Province (FJNU), 350117, Fuzhou, China
a
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Received:
30
July
2025
Accepted:
28
November
2025
Published online:
8
December
2025
Abstract
The occurrence of Parkinson’s disease (PD) is related to the interaction among various neuronal clusters and time-delays. They can cause different degrees of abnormal synchronous oscillations in the basal ganglia, such as the typical 
oscillation in PD. In this paper, a model of the basal ganglia (BG) with time-delay is studied. The pedunculopontine nucleus (PPN) and centromedian–parafascicular complex of the thalamus (CM/PF) as significant targets for deep brain stimulation (DBS) are considered in the model to investigate the oscillatory dynamics in PD. It has found that the time-delays between different neural nuclei will cause the system to shift from a stable state to a Parkinsonian state. Furthermore, the pathways connecting some neuronal nuclei can affect the activity of neuronal clusters in BG. Specifically, enhancing the coupling weight from the cortex to the PPN will intensify the oscillations in the system, while strengthening the connection weight from the cortex to the CM/PF can effectively suppress the oscillations. Additionally, modulating the output of the cortical excitation pathways or the feedback output between neural nuclei can cause the system to exhibit different oscillatory states, such as 
, , 
, 
, or 
oscillation. The different oscillation frequency of the nuclei in the brain has a significant impact on physiological functions, such as cognition, emotion regulation, and sleep. Therefore, the results obtained in this paper will help to understand the pathological mechanism of PD and inspire further experimental and modeling studies in the field.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Yanhong Zheng, Qiuping Chen, Linnan Ma, and Jian Zeng have contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
