A Physical Model Of The Development Of Neural Networks In Brain

Rencently,with the development of neural networks,neural networks are considered as complex networks by scientists.Some experiments demonstrated the saturated time of synapses,theoretical results suggested neural distance distribution between connected neurons exhibits pow-law distribution.In this thesis,through the approach of complex network,we investigate the growth development of neural networks in brain.In the first chapter,we review the fundamental concepts of complex networks,neural networks in brain and brain functional networks.In the second chapter of this thesis,based on two neuronal experiments in vitro by Japanese scientists,according to the biological characteristics of neurons,we make up a model of the growth development of neural networks.We have used different initial cultured densities and different cultured size to simulate properties and characteristics of neural networks.In the third chapter,the results demonstrate that we have reconstructed the growth development progress of neuronal networks in vitro successfully.The parameter conditions for essential consistence between simulated saturation time of synaptic number and cultured experimental results in vitro have been found out.The main results include:(1)Neuronal density decreases as time,and it goes to a stable value gradually after certain days;(2)The number of synapses between neurons increase as cultured time,then it saturates,which essentially fits experimental data;(3)By statistical analysis over distance between connected neurons,within the parameter range with consistence between simulated synaptic saturation time and experiment results,no power-law distance distribution proposed by Karbowski is verified,instead,exponential decaying distance distribution is obtained.Among them,Results(1)and(2)are consistent with experimental results,while result(3)is expected to be verified by future experiments.The last chapter contains the summary of this thesis and the analysis of defect of the model.