Chaos Synchronization And Order Emergence In Multi-Layer Center Dynamical Networks

Multi-layer center networks are a class of typical networks in the world, in this dissertation we study the property and dynamical behavior of multilayer center networks. Three-layer center networks are more representative than one-layer and two-layer center networks, so we emphasize on three-layer center networks in our analysis.We apply dynamical systems theory and numerical analysis method to study the synchronization of three-layer center networks, explaining the relations between topological structures and synchronization. In our study, by using linear stability analysis approach, we discuss several different coupling schemes of three-layer center networks with the Logistic map local dynamics, and obtain the range of coupling strengthεwhen the whole network achieves complete synchronization. We prove the eigenvalues of the coupling matrix are all real, at the same time, we find that the second and the third layer centers play an important role in the synchronizing process. Furthermore, our numerical results show that multi-layer center networks have self-organization effect on changing the dynamical behavior from chaos to order. Finally, we summarize the results and list some problems for further research in the future.