Synchronization of coupled system

The phenomenon of synchronization is present in many situations of our everyday life. In order to describe this phenomenon we assume to have n identical mechanical or biological systems.ın all the papers that I reserched only linear couplings of various kind are considered.In this thesis we shall generalize their result so as to obtain synchronization for n identical nonlinearly coupled system. In this thesis organized as follows. In chapter 1 we give general information about sysnchronization. In chapter 2 we recall some basic definitions and properties of abstract dynamical systems. In chapter 3 we consider the problem of complete synchronization of global solutions of the n coupled identical system. In chapter 4 we prove that under certain auxilary assumptions on f system possesses a compact global attractor. In chapter 5 we describe a biological model to which our analysis can be applied.