Study On Excitement Characteristics And Stochastic Resonance Of Complex Biological Neural Networks

It has passed more than 10 years that Watts and his tutor Strogatz proposed the small world network effects. However, people's enthusiasm of exploring complex network has not been abated. The research of complex network has been involved in various fields, in which research on biological neural network is one of the focuses of attention. In the life sciences field, the most exciting thing is to understanding people themselves. The questions that how to understand human behavior and know the mysteries of the brain look very simple, but these are very difficult for us to answer. We now know that neurons are the most basic units of signal transduction. So, to understand the physiological basis of human behavior, we must understand the neuronal signal transmission characteristics. And further, up to the network level, if we understand signal response of the biological neural networks, it may further help us find some clues of those issues.This paper mainly discusses the issue of the signal response of biological neural network. The main results include the following.The link between excitatory of neurons and neuronal electrical phenomenon is very close. It is very meaningful to study the overall excitement of biological neural networks. And according to complex network theory, the small-world effect and the scale-free characteristic exist in the many real-world networks. We take them as basis and set up two complex network models that have these characteristics. We study excitement of these two models and the stochastic resonance phenomenon of one model.Firstly, we have set up the small-world network whose nodes kinetic equations are HH equations and in which the lateral inhibition and the growth and decay mechanism are introduced. From the numerical simulation, we find that in a growth phase mode the biological neural network will show extremely "not excited". And the saturated effect is also found as the increasing frequency of external stimulation. The excitement of neural network is becoming "stronger" as increasing noise intensity and coupling strength. At the stage of aging mode,the saturated effect was found with increasing frequency of external stimulation in the neural networks. As the noise intensity and the coupling strength increased, the neural network excitement was becoming "weaker".Secondly, we have built the scale-free network whose nodes kinetic equations are HH equations and in which we thought that the weights of networks were impacted by noise. Neural network will show two phenomenons at specific frequency: "extreme excitement" and "not extreme excitement". And the saturated effect is found with the increasing frequency of external stimulation in this mode. As noise intensity increased, the inhibitory effect was found in this network. However, the excitement level of the entire network was becoming stronger with coupling strength increased.Thirdly, stochastic resonance phenomenon can be found in the nervous system. This means that nervous system may improve detection capabilities of outside weak signal by using stochastic resonance mechanism. The mode we use is the same as above- mentioned. (â… )Weak signal detection capability of the variable weight neural network is stronger than that of the unchanged weight network. (â…¡) In the variable weight neural network, when the coupling strength was certain, detection of weak signals in different networks size converged gradually with the noise intensity increasing, and when the noise intensity was certain, matching range is up to max when networks size are at certain degree with some certain coupling strength. (â…¢)There is a satisfactory range of weak signal detection in nonlinear system in specific networks architecture parameters.