The response of nonlinear systems to noise is very interesting research topic. Especially, stochastic resonance (SR) has attracted large attention during the last two decades. The basic result of SR shows that the response of a nonlinear system is optimized at a certain finite level, neither very weak nor very strong, of noise. Here, optimized response means that a system detects very weak signal aid by optimal noise and can show most coherent motion aid by optimal noise. The SR phenomena have emerged in many fields, from physical to biological systems. In particular, SR has been studied very extensively due to an application in information process of neuroscience.
In this thesis, we investigate the response of neural network to noise for two neuron models with numerical method. Previous studies have been conducted on regular or fully random network mainly. But it is well known that biological neural network present a clear clustering in their neurons but have small distances between each pair of neurons. This kind of network is known as small-world network. Therefore, throughout this work, we employ Watts-Strogatz small-world network as a connection topology.
Firstly, we investigate the coherence resonance (CR) of Hodgkin-Huxley neurons. It is found that increasing the randomness p of the network topology leads to an enhancement of temporal coherence and of spatial synchronization. Especially, it is found that (1) spatial synchronization increase as characteristic path length L shortens and (2) firing frequency increases as clustering coefficient C decreases. We introduce constant-clustering network. In such a network, synchronization increases as L shortens, but firing frequency remains constantly. This result leads to more confidence of above relations.
Secondly, we study the effect of spatially correlated noise on CR in neural network of Fitz Hugh-Nagumo neurons, where the noise correlation decays exponentially with distance between neurons. For intermediat...