Multi-Scale Dynamics And Microscopic Mechanisms Of Cerebral Cortical Networks

The human brain is one of the most complex network systems in the universe.It contains about 1011 neurons and 1015 synapses.Its complexity far exceeds our current cognitive capabilities,so it is difficult to study such a complex system with traditional methods.Therefore,using the knowledge and methods of complex networks to study brain networks has become an effective way to understand the brain.From the perspective of brain structure,brain networks exhibit complex topology.Notable network features of the topological organization of structural connectivity（the connectome）are small world,communities,hierarchical and rich-club connectivity.From the perspective of dynamics,there are very rich dynamic patterns in the brain.These dynamic patterns are considered to be the emergence of collective dynamic behaviors generated by neurons through synaptic interactions,which are closely related to cognitive function of the brain.Although functional interactions are shaped and constrained by the underlying anatomy,the precise nature of the relationship between structure and function remains a fundamental question.Therefore,in this thesis we use the research methods in complex networks to explore the diversity of dynamics in brain networks and underlying physical mechanism.And we hope that our research results can trigger a follow-up research boom.First,we found that adaptive coupling can induce chimera states in neuronal dynamic systems.The patterns of these chimera states may be different and abundant,depending on the different network topologies such as the fully connected,random,and scale-free networks.In particular,we apply this adaptive model to the realistic network of cerebral cortex and interestingly find that the adaptive coupling can also induce a diversity of chimera states,which may provide a new insight for the high capability of flexible brain functions.Moreover,we find that the preference of observing chimera states in heterogeneous networks is greater than that in homogeneous networks,and the latter is greater than that in the fully connected network,which may be one of the reasons for the nature to choose the specific sparse and heterogeneous structure of our brain networkSecondly,Using coupled neural mass oscillators on human cortical network and paying attention to both global and local regions,we observe a new feature of chimera states with multiple spatial scales and a positive correlation between the synchronization preference of local region and the degree of symmetry of the connectivity of the region in the network.Further,we use the concept of effective symmetry in the network to build structural and dynamical hierarchical trees and find close matching between them.These results help to explain the multiple brain rhythms observed in experiments and suggest a generic principle for complex brain network as a structure substrate to support diverse functional patterns.Thirdly,we study the time-limited self-sustaining oscillatory patterns in brain networks,which have the characteristic features of multiscaled rhythms and frequent1y switch between different rhythms.In order to understand its mechanism,we present an approach of dominant activation paths and find that the multi-scaled rhythms can be separated into individual rhythms denoted by different core-networks and the switching between them can be implemented by a time-dependent activating threshold.Further,based on the microstates of time-limited self-sustaining oscillatory patterns,we present a new concept of return-loop to study the distribution of the return-times of microstates in time-limited self-sustaining oscillatory patterns and find that it satisfies the Weibull distribution.Finally,we use the eigenmode method to study the relationship between the brain structure network and its dynamic behavior,and use the local eigenvectors to construct eigenvector patterns consistent with the dynamical patterns behavior of the brain.