Synchronization is one of the most important phenomena in science such as sociology, biology and physics. Synchronization is a fundamental concept in chaos and dynamical systems. Chaotic systems are those which are sensitive to initial conditions and their future behavior cannot be predicted exactly . Dynamical systems left; LINE-HEIGHT: normal; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: rtl" dir=rtl align=right There are two kinds of synchronization, global and local. Stability of synchronization state is the ability of the system to return to its normal state when we introduce perturbation. For study of the stability of synchronization state, we use two methods: 1- master stability function, 2- matrix measure approach. Master stability function mostly is used in continues systems and matrix measure approach in discrete systems. In master stability function method we need to know the oscillators equation and the chaos parameter, but in the matrix measure approach we need just to know coupling matrix. Master stability function gives us necessary and sufficient conditions but the matrix measure approach gives us sufficient conditions. One example of discrete systems are Logistic maps. We simulate these maps on the Scale Free network, the Regular network, the Small World network and the Erdos-Renyi network and study the synchronization conditions and stability of synchronous states. To this aim, we use the master stability function and the matrix measure approach. At the end we compare these systems and discuss the conditions of the systems to be whether synchronized and stabilized or not.
