Research On Several Kinds Of Complex Network Synchronization Based On Several Control Strategies

Complex networks, indeed, are so ubiquitously found in nature and in the modern world, from the brain structure to metabolic networks, from the Internet to the World Wide Web, from powder networks to complicated tra?c networks, from the scienti?c collaboration network to the social networks of business or economic relations, and so on. The study of dynamics in complex networks has been focused from different disciplines. Synchronization is a foundation to be used to explain the numerous coordination behavior in nature. It has become one of hot topics in the researches of complex networks due to its challenging theory and extensive application. Based on the theory of complex networks and dynamical systems, the main aim of this paper is to study the synchronization problem of several class of complex networks by using pinning, periodically intermittent pinning and impulsive control in modern control theory. We also establish the moving pulse-coupling oscillators network model and discuss its synchronization mechanism. The main contributions of this paper are listed as follows.First, the linearly coupled complex networks with and without time delays coupling has been extended to nonlinearly-coupled complex networks with and without timevarying delays coupling. The M-matrix strategy is used to derive su?cient conditions for this new proposed network by applying a feedback control input to a small subset of nodes. Out result is a nontrivial extension of the existing result. In order to ?nd a sharp bound for this coupling strength, take the coupling strength of the network as continuous differentiable function of time. The adaptive law designed is more reasonable and the synchronization of the network is realized under the condition of the coupling strength as small as possible. We give numerical examples to illustrate the effectiveness of our theoretical results, Noting that the ?nal adapting coupling strength is smaller than its theoretical value.Secondly, considering that complex systems are noisy, the exponential synchronization is investigated for stochastic complex networks, where time-varying delays exist in the dynamics of nodes, the coupling and the noise strength matrix. By utilizing the Lyapunov stability theory, stochastic analysis theory as well as linear matrix inequalities, the su?cient conditions are derived to guarantee the exponential synchronization via periodically intermittent pinning control, which is a feedback control input applied to a small subset of nodes at some discontinuous and periodic time intervals. The synchronization of the model depends on not only the topological structure of the network and time-varying delay, but also the number of pinned nodes, the control period and control width. The numerical simulation of 2D chaotic delayed neural network is provided toshow the effectiveness of the theoretical results.Furthermore, the connection relation between nodes in a network is evolving, this is to say, the topological structure is time-varying. Based on the characteristic, We extend the above model to a class of stochastic complex networks with Markovian switching and time-varying delays. The switching parameters are modeled by a continuous-time,?nite-state Markovian chain and the complex network is subject to noise perturbations,Markovian switching and internal and outer time-varying delays. The synchronization problem of the proposed stochastic complex networks is investigated by using pinning control scheme in Chapter 5 and impulsive control scheme in Chapter 6. The bene?t of the impulsive control is a feedback control input applied at discrete-time instants and can reduce the control and communication cost. Su?cient conditions for the mean-square exponential synchronization are obtained through employing the Lyapunov functional, It?’s formula, the linear matrix inequality and impulsive control theory. Numerical examples are also given to demonstrate the validity of the theoretical results.Finally, we present the synchronization of a population of identical moving pulsecoupled oscillators that are con?ned to move in a plane with mutual interactions, which are controlled by some pre-determined state threshold values and only take effect inside some known communication radii. The states are allowed to evolve in a nonlinear and periodical manner in accordance with a smooth, monotonically increasing and concave down function. The model is initially inspired by synchronous ?ashing of ?re?ies and integrated both the oscillators’ mobility and pulse coupling. The effect of pulse signal on synchronization is explored in detail. Su?cient conditions are established for synchronization. Our result is a nontrivial extension of the pulse-coupling oscillators, where the oscillators are stationary and the network is fully connected. In numerical simulation,the dynamics of the oscillators in our network are modeled by Peskin’s model, and the general effects of system parameters on the synchronization rate are further probed into. It is found that increasing signal strength causes the synchronization rate to initially decrease,then remain almost constant, then increase again until it ?nally decreases.Furthermore, with increasing speed modulus the synchronization rate initially decreases then increases. The synchronization rate, however, decreases with an increasing communication radius. Finally, as a real-world application, the proposed model is used to synchronize the different clocks in an ultra-wide bandwidth wireless ad hoc network. The numerical examples illustrate the effectiveness of the theoretical results.