In this paper,we investigate the evolution of spatiotemporal patterns and synchronization transitions in dependence on the information transmission delay and ion channel blocking in scale-free neuronal networks.As the underlying model of neuronal dynamics,we use the Hodgkin-Huxley equations incorporating channel blocking and intrinsic noise.It is shown that delays play a significant yet subtle role in shaping the dynamics of neuronal networks.In particular,regions of irregular and regular propagating excitatory fronts related to the synchronization transitions appear intermittently as the delay increases.Moreover,the fraction of working sodium and potassium ion channels can also have a significant impact on the spatiotemporal dynamics of neuronal networks.As the fraction of blocked sodium channels increases,the frequency of excitatory events decreases,which in turn manifests as an increase in the neuronal synchrony that,however,is dysfunctional due to the virtual absence of large-amplitude excitations.Expectedly,we also show that larger coupling strengths improve synchronization irrespective of the information transmission delay and channel blocking.The presented results are also robust against the variation of the network size,thus providing insights that could facilitate understanding of the joint impact of ion channel blocking and information transmission delay on the spatiotemporal dynamics of neuronal networks.
The persistence of beta oscillations generated in the basal ganglia is typical pathological characteristic of Parkin-son's disease.In this paper,we construct a new network model,which is mainly composed of the subthalamic nu-cleus and the globus pallidus.Based on theory analysis,we obtained the beta shock conditions in the proposed model.It is shown that numerical simulations are in good agreement with analytical results.At last,the effects of cortex and striatum inputs on the generation of oscillations are also discussed.We hope that the obtained results may find applications to treatment of Parkinson’s disease and study of neural oscillations produced in other parts of the brain neural network.
