The investigation of dynamics of scale-free network consisting of biological neurons

Nervous system, consisting of billions of neurons and links between them, has a complex structure. In this complex structure, neurons are in the sub-groups which have different functional roles. In this context, complex network models which are used in order to explain information processing and transmission mechanisms of nervous system, are widely used to modeling the complex network topologies. The scale-free network model is one of the network models benefited for modeling of the connection topologies of functional brain regions.In this doctorate thesis, processing and transmission of neural information and neural synchronization issues are discussed in scale-free networks by using a more biophysically realistic model of neurons. Each nöron in the network is modeled including ion channel noise originated from stochastic nature of ion channels depending on cell size. In this work, the determination of necessary conditions for optimal coding of weak periodic signals is firstly investigated. It is determined that ion channel noise stemming from internal dynamics of neurons, frequency of weak periodic signal, average degree of network and coupling strength must be at their optimal values for the best coding of weak periodic signals. Besides, in this study transmission of weak periodic signal in scale free networks is studied and regardless of location of neuron introduced weak periodic signals optimal transmission of weak signals are obtained when the ion channel noise at appropriate levels. In addition, improvement of weak signal transmission is obtained on the appropriate information transmission delay times.Finally, in this work, effects of information transmission delay on the temporal and spatial synchronization of neurons on scale-free networks is investigated. With the increasing of information transmission delay, different synchronization transitions of neurons are observed on scale-free networks. Additionally, on the fine tuned delay times an enhancement of spatial and temporal synchronization have been observed.