OSCILLATION DYNAMICS ANALYSIS OF PARKINSON'S MODEL WITH TIME DELAY

The study of the origin of abnormal beta oscillations generated in the basal ganglia of the brain can help analyze the pathogenesis of Parkinson's disease. In this paper, the oscillatory dynamics of a modified cortico-basal ganglia (E-I-STN-GPe-GPi) resonance model is systematically investigated. First, the conditions for the stability of the model at the local equilibrium point and the occurrence of Hopf bifurcation are obtained by the Routh-Hurwitz criterion and stability theory, and the range of time delay parameters for the existence of Hopf bifurcation in this resonant model is derived. It was found that increasing the time delay of synaptic transmission could generate Hopf bifurcation in the model and induce beta oscillations, allowing the system to switch between the healthy and Parkinson's disease states.Second, it was revealed that the generation of beta oscillations is related to the strength of synaptic connections associated with the subthalamic nucleus. From the results of numerical simulations, it can be seen that when the subthalamic nucleus is subjected to both excitatory neuronal clusters and stronger facilitation of the globus pallidus external, oscillations are generated. Finally, the effect of GPi-related parameters on its generation of oscillations was analyzed by numerical simulations, and our results revealed that when smaller GPe synaptic connection strengths and larger synaptic transmission time delay are combined, they are more likely to make GPi oscillate with increasing amplitude. It is hoped that the results of this paper can provide some reference for the study of the mechanism of Parkinson's disease.It is hoped that the study of the dynamics characteristics of the E-I-STN-GPe-GPi resonance model in this paper will help us understand the pathogenesis of Parkinson's disease and reveal the origin of abnormal beta oscillations in Parkinson's disease.