In this paper, we integrate impulsive control and adaptive control methods, based on the stability theory of impulsive differential equations, generalized projective synchronization between the general complex dynamical networks with time delay is investigated. A nonlinear controller, updating laws and a linear impulsive controller are proposed. An adaptive-impulsive generalized projective synchronization criterion of network with time delay is established. Moreover, the complex network with time delay consisting of energy resource system is used as a numerical example. Generalized projective synchronization between two energy resource complex networks with time delay is achieved. This study will be instructive for the demand-supply of energy resource in some regions of China.
The ultimate state of projective synchronization is hardly predictable. A control algorithm is thus proposed to manipulate the synchronization in arbitrary dimension. The control law derived from the Lyapunov stability theory with the aid of slack variables is effective to any initial conditions. The method allows us to amplify and reduce the synchronized dynamics in any desired scale with tiny control inputs. Applications are illustrated for seven- and ten-dimensional chaotic systems.
Several sufficient conditions which guarantee stability of linear time-delay systems are derived. Each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness.