Synchronization And Application In Excitable Neural Systems

The rhythm phenomena of brain electrical activity can be understand under the frame of coupling oscillator, it gives some explanations for large numbers of synchronization phenomena and correlative behavior to be observed in neuron system. In life system, the synchronization is necessary for normal function, such as the communication among the different function regions, but the abnormal synchronization will result in serious out-of-order, such as recessive neural diseases: Epilepsy and Parkinson. That is main content in this thesis to investigate synchronization oscillation of excited neuron network and neural electrical activity. The mainly instrumentality used in this thesis is the method of nonlinear and complexity. This study is usefull to know the complicated dynamic behavior of network, which is formed by coupling among neurons, and usefull to explore the mechanism of abnormally neural activity in Epilepsy outbreak and so on. Main work in this thesis as follows:1. Synchronization and coupling parameter of multilayer global coupling and small world McCulloch-Pitts neural networksTo study synchronization and coupling parameter of multilayer global coupling and small world McCulloch-Pitts neural networks, we extend the result reported by literature, which investigated double-layer McCulloch-Pitts neural networks. An exponential decay form between critical coupling intensity and network scale is observed in the multilayer global coupling and small world McCulloch-Pitts neural networks; The larger linked degree becomes, the larger critical coupling intensity becomes. It is more and more difficult to come true synchronization with the network scale going up, namely larger coupling intensity is necessary. The relationship between critical coupling intensity and linked degree closes to sigmoid curve. The oscillation phenomena in the relationship of critical coupling intensity and the number of neural networks layers in the case of small-scale networks are found. We obtain the synchronization diagram on the parameter plane of the number of neural networks layers and the network scale in multilayer global coupling McCulloch-Pitts neural networks.2. The desynchronization of excitable neural network and the influence of the pulse stimulating parameters on the desynchronizationTo simulation study small world HR neural network and global coupling HH neural network, we find that synchronization of neural network evolves into desynchronization when a part (about 10 percent) of neurons are stimulated with a pulse current signal. The higher the stimulation frequency is, the larger the degree of desynchronization. The network desynchronization appears to be sensitive to the stimulating frequency and intensity. This is consistent with the clinical experimental results of vagus nerve stimulation therapy for patients with refractory epilepsy. The de-synchronization of larger stimulation intensity to network is more distinct than that of weaker stimulation intensity. At the same stimulation intensity, the desynchronization of network is more prominent with small coupling intensity than that with larger coupling intensity. We find that there exist the optimal stimulation interval and optimal period of continuous stimulation time when the other stimulation parameters remain certain.This study above is usefull to explore the theoretic mechanism for vagus nerve stimulation therapy for patients with refractory epilepsy; and usefull to offer some warranties for selecting stimulation parameters in vagus nerve stimulation therapy for patients with refractory epilepsy.