Outer Synchronization Of Driven-Response Complex Via Intermittent Control

Complex networks are widely existed in human society and nature. In recent years, the research of complex network mainly focused on its dynamical behaviors. The problem of network synchronization has received much attention by researchers and become a hot topic. Due to its great research value, outer synchronization between two complex networks has attracted considerable research interest. This article investigates the outer synchronization problem of the driven-response complex networks via periodically intermittent control:1?The problem of periodically intermittent pinning outer synchronization between delayed driven-response complex networks with nonlinear coupling is studied. Both the internal delay and coupling delay are included in coupled network model. By designing appropriate adaptive periodically intermittent controllers and using the Lyapunov stability theory, some pinning outer synchronization criteria are derived, which can guarantee the response network asymptotically synchronizes to drive network. Simultaneously, two simple adaptive intermittent pinning outer synchronization conditions are obtained based on the proposed criteria. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results.2?By using the intermittent control with two different switched periods, the problem of the lag synchronization between the driven-response complex networks is studied. These two switched periods may have different control rates. By designing appropriate adaptive intermittent pinning controllers and using Lyapunov stability theory and rigorous mathematical proof, some sufficient conditions for ensuring the lag synchronization between two coupled networks are derived. The minimum number of pinned nodes is determined by node dynamics, coupling strength and a design parameter. Two numerical examples are given to illustrate the feasibility of the theoretical results.3?The problem of finite time outer synchronization of driven-response complex dynamical networks via periodically intermittent control is studied. By designing appreciate intermittent controllers and using finite time theory, differential inequality technique and the linear matrix inequality, the finite time synchronization criteria are obtained, which can lead o a smaller setting time. Finally, numerical example is given to illustrate the effectiveness and correctness of the theoretical results.