Research On The Dynamics Of The Coupled Neuronal Networks With Synaptic Plasticity

The nervous system is a large information system that produces sensation, learning, memory and thinking. In the cognitive process of human brain, the synchronization and the rhythm dynamics are closely related to the transmission and processing of information. The real neuronal system is a nonlinear dynamic system, so we should not only consider its highly nonlinearity and complexity, but also discuss its time-varying property, robustness and vulnerability. One of the most important issues involved in learning and memory is synaptic plasticity.Therefore, the dynamics of coupled neuronal system with synaptic plasticity is studied by using the theory of nonlinear dynamics and numerical method in this thesis.In this thesis, we construct a neuronal network which agrees with the actual biological neural network. The effects of the topological structure of the neuronal network, the coupling strength between neurons and the coupling mode on the synchronization and rhythm of the network are discussed. We hope numerical results we derived to be helpful to understand the dynamical mechanism of coupled neuronal system, and to guide electrophysiological experiments in the future.In the first chapter, we introduce some background knowledge and current related researches. Then, the purpose and content of this thesis are described in detail. Finally, the basic knowledge of this thesis is introduced.In the second chapter, we mainly discussed the synchronization and rhythm dynamics of the small world and globally coupled neuronal networks. Numerical results show that in both globally coupled network and the small world network, the synchronization can be enhanced with the increase of synaptic connection strength. With the increase of time delay, the number of 'spikes' in one burst will increase gradually at the integer multiple period of T, the frequency of the neurons would be in mixed oscillations. When the delay is long enough in the globally coupled network, the low-frequency rhythm is mainly theta oscillations,which is associated with the sleep state. The high frequency rhythm is always gamma rhythm. When the delay of small world network is long enough, the frequency of neurons will be alpha and gamma oscillations.In the small world network, when the synaptic strength is the same, the synchronization state increases with the increase of the connection probability. For the fixed connection probability, the synchronization increases firstly and then becomes stable, which indicates that synaptic plasticity and network topology are important for network synchronization.In the third chapter, we studied the effects of noise and synaptic plasticity on Izhikevich neuronal models. The dynamic behavior of neural networks is analyzed, and the specific effect of the synaptic plasticity on the neuronal network is discussed quantitatively. In the nervous network, the coupling strength of neurons will fluctuate regularly with time, but in a time period, the average coupling strength of neurons is stable. These phenomena are consistent with the reality of the biological nervous system, so synaptic plasticity is essential and important for the neuronal network. At the same time, the presence of noise can change the coupling strength between neurons and promote synchronization at the initial time, which further implies that noise has a positive impact on coupled nonlinear systemsIn the fourth chapter, we summarize the results of this thesis.