| Neuronal oscillations are an essential characteristic of the brain dynamics and can be found in the whole brain network.According to the different frequency bands,they can be separated as α rhythm(8-13Hz),β rhythm(13-30Hz),γ rhythm(30-80Hz)etc.The synchronous activity of oscillating networks and the sequential movement in space of oscillating networks are thought to be important mechanisms linking singleneuron activity to functions and behaviors.In this thesis,first,I focus on the mechanisms of neuronal rhythms,particularly the beta rhythm observed in the primate motor cortex.Then,I investigate partial synchronization such as chimera states and remote synchronization based on the human cerebral cortex network.Beta oscillations(13-30Hz),which are observed in monkeys when they are trained to perform a delayed reach-to-grasp task,are prominent during movement preparation.Beta oscillations are sporadic and organized into complex patterns(e.g in planar,radial,spiral waves).In order to study the origin and characteristics of beta oscillations,we propose a simple model of the motor cortex based on local excitatory-inhibitory neuronal populations coupled by longer range excitation.These modules also receive additional stochastic inputs from other neural structures.We separate the stochastic inputs into two parts: one is local and varies from module to module,and the other is global and consistent across all modules.We have shown that this model can accurately reproduce the statistics of recording data when these external inputs are correlated on a short time scale(～ 25ms)and the two different components of external inputs are appropriately weighted.The model reproduces the distribution of beta burst durations,the proportion of the different observed wave types,and wave speeds.It also serves to provide a theoretical analysis of beta oscillations.Chimera states represent the coexistence of coherent and incoherent dynamics.They are thought to be related to the unihemispheric sleep of some birds and marine mammals and to the first-night effect of human beings.We present a two-layered network of coupled neurons(each layer represents the left and right hemispheres of the cerebral cortex,respectively,and the links between the two layers represent the intercouplings through the corpus callosum)to study the collective patterns of the brain network.This simplified model allows us to find chimera states for brain networks.Further,we investigate the general two-layered network and study how structural parameters shape the dynamics of the network.We also consider the effect of delay due to the limited speed of signal transmission by distinguishing the inter-and intra-couplings as chemical synapse couplings and electrical synapse couplings,respectively.Remote synchronization is characterized by the synchronization of pairs of nodes that are not directly connected via a physical link or any sequence of synchronized nodes.It is thought to take a key role in supporting the segregation and integration of brain functions.Based on the real network of the human cerebral cortex,we show that remote synchronization can be observed in networks of identical oscillators,provided that an appropriate time delay is considered.We propose a new framework of multiple starlike graphs connected by common leaf nodes to understand the mechanism of remote synchronization.We further show that the common leaf nodes take a key role for the emergence of remote synchronization. |
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