Intermittent Nonlinear Differential Delayed Feedback for Suppressing Synchronous Oscillations of Parkinsonian State
Hongpeng Yang, Jiang Wang, Yuxin Wang, Chen Liu · 2025
Abnormal synchronous oscillations in the basal ganglia are a hallmark of the Parkinsonian state. Suppression of heightened beta-band ($13-35 ~\text{Hz}$) oscillatory activity is associated with alleviation of hypokinetic motor symptoms in Parkinson's disease (PD). Nonlinear delayed feedback has proven to be a powerful method for disrupting pathological synchronization. In this paper, we develop a basal ganglia-thalamus (BG-TH) network model to simulate neuronal dynamics characteristic of Parkinsonian state. Using mean-field theory, we model three neuronal nuclei and apply differential nonlinear delayed feedback. Numerical simulations indicate that this strategy effectively reduces the order parameter and mitigates abnormal synchronization. Differential feedback scheme exhibits heightened sensitivity to variations in feedback parameters, while maintaining lower intrusiveness, as the feedback signal generally remains close to zero. When feedback signal is removed, differential feedback maintains the control effect and continues to suppress oscillations for a period, providing control continuity. Thus, considering its capability for oscillatory suppression, minimal intrusiveness, and continuity, this paper proposes an intermittent nonlinear differential delayed feedback stimulation scheme. The results show that this scheme can provide good inhibition of abnormal synchronous oscillations of neurons while reducing the invasiveness of the stimulus signal.