| Birds of a feather flock together. Community structure exists in many large-scale complex systems consisting of large number of interactive individuals, such as, ecological network, scientific research cooperation network, neural network, and so on. Community networks are usually adopted to describe these systems with community structure. The individuals in the same community often have the same or similar function and goal, and the connections among them are dense. However, the individuals in the different communities often have different function and goal, and the connections among them are sparse. This kind of collective dynamical behavior called cluster synchronization.Due to the complexity of real systems themselves, community networks usually cannot synchronize themselves without external control. Thus, many control methods are introduced to design effective controllers for achieving cluster synchronization, including feedback control, impulsive control, intermittent control, finite-time control, and so on. In practical applications, the goals are expected to be achieved in finite time. Therefore, finite-time control method is widely adopted to study synchronization control issues of different networks.This thesis mainly studies the cluster synchronization of community networks based on finite-time control theory and Lyapunov stability theory. Chapter 1 introduces the research status and presents some preliminaries. Chapter 2 investigates the cluster synchronization of real-variable community networks without and with coupling delay, designs effective finite-time controllers, derives the sufficient conditions for achieving synchronization and performs some numerical examples to verify the effectiveness of the obtained results. Chapter 3 studies the cluster synchronization of complex-variable community networks, provides the synchronization criteria and performs numerical s imulations. Chapter 4 concludes this thesis and points out our future possible works. |
PDF Full Text Request