The Applications Of Nonlinear And Complex Network Methods In The Neural Dynamics And Hemodynamics

Life is related to nonlinearity, hiberarchy and network from the point view of complexity science. The nonlinear and complex network methods are very important in the study of life science. It is prospective that new hints will be found for the pathogenesis and diagnosis of nervous system disease and cardio cerebrovascular disease if these two methods are applied to the investigation of neural dynamics and hemodynamics.Based on the methods of nonlinearity and complex network, issues related to the neural dynamics and hemodynamics are analysized by numerical simulations and experiments. The main work and contributions in this study are summarized as follows:(1) Used Hindmarsh-Rose neuron as the node and constructed the network according to the Hopfield rule, considering the actual circumstance in the brain, pattern segmentation was studied in the weak, medium and strong connection strength, and good results were obtained via numerical modeling. At the same time, we studied pattern segmentation under random connection.(2) Proved the modulation of nonlinear coupling feedback on recovery variable equation to chaotic synchronization of two Hindmarsh-Rose neurons, the stability of synchronization has been validated by the calculation of the maximum conditional Lyapunov exponent.(3) Discussed the chaotic synchronization of Hindmarsh-Rose neural networks with nearest-neighbor diffusive coupling form using developmental SC method. For three and four neurons network,a certain region of coupling strength corresponding to full synchronization is given, and the effect of network structure and noise position are analyzed. For five and more neurons network,the full synchronization is very difficult to realize. All the results have been proved by the calculation of the maximum conditional Lyapunov exponent.(4) Used EEG data to extract functional networks connecting correlated human brain sites. Analysis of the resulting network shows statistical characteristic of complex network.All these properties reflect important functional information about brain states. To alcoholic, the characteristic index of their brain is obviously different from control. Brain neural network information entropy and brain neural network normal information entropy are also defined to measure the complex network characteristic. A criterion in diagnosis and therapy of clinical encephalopathy is given. Calculating result illustrate that the brain neural network information entropy of alcoholic is quite distinct from control.(5) The data from the experiments of low blood flow and hypertension in artery of rats were be used to calculate the Lyapunov exponent of carotid artery blood flow time series including normotensive and hypertensive rats, which may be a new idea to appraise the inherent correlation among hypertension, atherosclerosis and cerebrovascular diseases.