Stochastic Dynamics Behavior Of Coupled Neural Networks

The Hodgkin-Huxley model which was raised by Huxley and Hodgkin in1952not only laid a theoretical foundation for the study of neurons dynamics but also explained all kinds of random dynamic phenomena about neurons,making the development of neural science became one of the most important events of the natural science in the1940s. The transmission of information between neurons is based on the releasing and transfering of the action potential in the neural network. Thousands of neurons form the coupling nervou system through the gap and synaptic connection, then the the coupling neurons carries the information by sequence of action potential,thus we reveal and explain some random dynamic phenomena by studying the coupling model of neurons. We study the influence under the ion channel noise in the coupling network about the nervous system dynamic behavior with the outside input by the computer simulation method.The main research contents are as follows:1. Introduced some basic knowledge about the neurons, including the structure of neuron, the development and classification of ion channels, the producing mechanism of action potential,etc. Given the single neuron Hodgkin-Huxley (H-H) equation and the coupling changing equation. Focused on two typical simulation methods according to the content of the research needs to describe the stochastic neuron system:Langevin and Markov.2. Studied the random characteristics of H-H model. Neurons will generate action potentials when the external input current exceeds the threshold.Neuron system is an incentive system, it can induce action potential because of the existence of noise in ion channel. Studied coherence resonance phenomenon considering the neuron existed in the environment of the noise with the outside input. The results of the study show that:(1) Ion channel noise is the main factor to arouse coherence resonance,and there is an optimal neuronal membranes area when the coherence resonance value is the maximum number.(2) The average response time increased with the increasing of membrane area when membrane area size is limited (limited ion channels the number).(3) There exist an optimal coupling strength corresponding to the most excitable system and the optimal coupling strength do not change with the different size of the neural network.3. Studied the stochastic dynamics behavior characteristics under the ion channels noise,and the influence to the frequency, the accuracy and the reliability of action potential. The results show that:The effect of ion channel noise increases firstly and then decreases but the error percentage and standard deviation decreases with the number of ion channels (which depends on membrane area in the same channel density) increasing.4. Studied the coherence resonance of the neural network after add the temperature factor into the transformation probability function of ion channels. Temperature is mainly effecting of ion channels switch chance to affect the entire nervous system,so basing on the Hodgkin-Huxley model, we add a temperature factor and compute the evolution of the neuron system by means of numerical simulation,to study the effect of temperature on neuron’s statistics property. The experimental results show that:(1) the increasing of temperature could make the ion channels open time reducing and the average duration time relies on the ion channel number or membrane area.(2) Lower temperature and more ion channels make the interaction more intense between the neurons about the neural network of the,and the coherence resonance coefficient also is greater.(3) The action potential might disappear due to the lower open chance of the ion channel causing by the higher temperatures,and the CR becomes very small, that means the coherence resonance may have been weakened when temperature is higher.