Synchrony is significant in brain neural network. Changes in synchrony can lead to cognitive dysfunctions in neural system. Synchronization is defined as an adjustment of rhythms of oscillating objects due to their weak interaction. An example of these phenamenon is the oscillating of fireflies, observation of firing in human neural network and synchrony in a collection of clocks. There are three complex networks and these are called regular, small-world and random networks. Small-world is one of the complex networks which is created by rewiring of the edges of a regular network with probability P and it is used to model neural. If the nodes of a network are selected randomly, we can get a small-world one. Two characteristics of small-world networks is short path length and large clustering coefficient. The degree distribution of the complex network is determined according to the type of the network and how it is constructed. Brain pathological state depend on the number of nodes. Deleting any node in alzheimer dieases is associated with increased path length or reduced global efficiency. There is a direct connection between cognitive dysfunction and changes in neural synchrony. In this situation $ ho$ which is called an order parameter, is decreased. Various methods are used to model brain with graghs. First approach is functional connectivity in which EEG, MEG and fMRI are used to connect edges and second one is structural connectivity. For example anatomical tract tracing of a brain is a usefull tool to map structural connectivity. The first approach lead to the undirected gragh and used to model a network. The model in which we apply to compute some statistical parameters is called Kuramoto and is defined as a coupled dynamical phase oscillators. To compute the phase of the oscillators, an Ewler method is usefull. Noise is a signal that varies as a function of time, the value of which at any time is drawn randomly from some distribution. Guassian white noise can increases neural firing rate and is effective in a production of a neural firing pulses. The correlation of the noise is a delta function. By calculating kuramoto order parameter and current, we can see collective firing induced by noise. Three dynamical regimes arise. no firing, in which all of elements confined near the fixed point, the second regime is a synchronized firing or coherent pulsation, where a macroscopic fraction fire simultanously, the third one is desynchronized firing or incoherent pulsation. By calculating an order parameter, we see that this parameter has a value less than one which means that this parameter depend on an initial condition and a complete synchronization is observed with fixed initial condition. Keywords: Synchronization, Firing, Noise, Excitable Media, Oscillatory
