Synchronization of continuous-time oscillators and its control

Abstract

In this thesis, synchronization of continuous-time oscillators with respect to the e ects which are bases on the network structure the properties of the oscillators and its control are studied. In the context of synchronization, synchronization of the periodic oscillators in di erent network topologies is considered. It is observed that the topological properties of networks are crucial for synchronization. Then, similarity-dependent coupling approach is introduced and the e ect of this formulation on synchronization is examined. Furthermore, synchronization in ensembles of chaotic oscillators is analyzed. In the control part, synchronization control is studied in ensembles of globally coupled chaotic oscillators. Two di erent control methods are proposed: time-delayed feedback and forcing with external periodic action. In the rst one, the mean- eld is fed back in a time-delayed manner to all oscillators. In the second one, cases are studied where an external periodic force is applied both to the mean- eld and to all the oscillators individually. It is observed that depending on the control technique and related parameters, synchronization can be enhanced, suppressed or destroyed. Another contribution of this thesis is a basic user interface for studying synchronization of continuous-time oscillators in complex networks.