The Complex Dynamics Of Neuronal Networks With Different Number Of Nodes

The purpose of neural network science is to reveal the mapping between the physical plane and cognitive plane, then reveal the nature and principles of biological intelligence work brain systems, ant it has become very important in the field of biophysics research. The most basic unit of structure and function of the nervous system is the nerve cell, also called neurons. The most basic function of nervous system is information or signal transmission by the electrical spiking neurons, not only including internal neuronal signal transduction from one location of a neuron to the other but all so including signal transduction between neurons. As early as the1950s, two scientists Hodgkin and Huxley had made famous Hodgkin-Huxley (HH) model on the transmission mechanism of an electrical behavior of a neuron.Neuronal system controls the majority of the body’s major life activities. Evolved after a long period, animals on Earth have formed the nervous system, which the developing and the complexity is increasing and the ability of adaptation to environment is growing in higher animals. Generally, the higher the animal is, the more the neurons number is and the more complex its nervous system, such as Aplysia neuron system consists of2000neurons and the human brain consists of about1011neurons. Perhaps it is because the brain has a huge amount of neurons so that it can complete a variety of advanced activity, showing many congnitive functions such as remarkable perception、language communication and learning and so on. This research prove the larger the neuronal network is, the more obvious the complex dynamics will be. It is well known that the neural network has a short path length and large clustering coefficient, namely real biological neural network module meet the small-world network structure. This thesis will build a small-world network model which includes nodes reflecting electrical behavior of an excitable neuron on the basis of the HH, and study the spiking synchronization and the stochastic resonance, and study the influence of the number of neurons on dynamics of small-world neuronal network.The main work of this thesis is as follows:(1) We introduced structure of single neuron, and analyzed its mathematical model that is HH equation and synaptic mathematical model,and simulated action potential case of neuron. After, we introduced the characteristics of small-world networks, and built small-word network and simulated the small-world network characteristics of the average shortest path and clustering coefficient.(2) It is studied the impact of white noise, synaptic conductance and the number neuron on the synchronization of synaptic coupled small-word neuronal network.Neural network is a complex nonlinear network, and includes a variety of noise:external white noise, synaptic noise, ion channel noise. First,we built a small-world network model containing ion channel noise and synaptic noise in the Microsoft Visual C++6.0platform, and treated random HH equation (Markov method) as a single neuron node model and used synapse coupled method containing synaptic noise, then we studied the influence of Gauss White noise and synaptic conductance and different number of nodes on synchronization of this neuronal network model. The results show that the synaptic conductance and white noise can affect synchronization of the neuron network, and noise intensity and synaptic conductance is suitable to make neural network optimal electrical spiking synchronization; synchronous neural networks with a huge neurons number is obvious, and the large network scale can promote the synchronization, which show that the ability of neural network complexity can affect the nervous system to receive the information and coding.(3)It is studied to the stochastic resonance of synaptic coupled small-word neuronal network and small-world network with different number neurons.Based on the stochastic HH neuron model, this paper structured a chemical synaptic coupled SW neural network including ion channel noise and synaptic noise, and studied stochastic resonance of this system. Taking into account the brain is a complex network composed of neural networks with different number neurons, this paper studied the stochastic resonance phenomenon of neuron network with different neuron numbers. The following results through numerical simulation:the noise can amplify the weak signal and induce stochastic resonance of nervous system, which overthrown that the noise was harmful to the nonlinear system and confirmed that the noise strength could make the neural system to achieve optimal stochastic resonance; the scale and complexity of the neural network can affect the stochastic resonance phenomenon, namely the more complicated and larger the network is, the greater the degree of stochastic resonance is, and this study result shows that the neural network size and complexity can influence the information processing ability of network.