ynchronization is one of the beauties of nature which has been seen in the collective behavior of complex physical, chemical, and biological systems. Neural networks, social interactions, and the Internet are examples of complex systems that coupled. By looking at the overall behavior of these systems, they can be considered as graphs which their dynamic elements are vertices of this graph and their weak links are graph edges.One common approach to examining the synchronization, is to consider system elements as phase oscillators with a weak coupling coefficient. In fact, synchronization is the tuned track of these oscillators. Along with the many models that have been presented in the past to examine this phenomenon, one of the easiest and most comprehensive models is the Kuramoto model.In most of the previous studies, the first-order model was used to investigate this subject. Taking into account the results presented by this model, the synchronization occurs a little faster than experimental observations in nature and biological samples such as firefly creams. The idea that completing this model with a damping and also inertia as a factor in changing the frequency of oscillator movement, caused suggestion of second-order Kuramoto model. In our study, a variety of complex networks has been selected that can be modeled with biological networks. In this thesis we first reviewed the previous works by applying the first-order Kuramoto model on a variety of networks. Then, with the use of the second-order Kuramoto model, we studied the impact of damping coefficient on the synchronization of different networks and finally we evaluated the system's state in different conditions.