Projective synchronization of a class of delayed chaotic systems on networks

We study projective synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where dynamical systems of single node must be partially linear. In this paper, the dynamics of the nodes of the complex net works composed by a large number of interconnected components are time-delayed chaotic systems without the limitation of the partial-linearity. Our work presented in this paper also can be considered as an extension of the dynamics of single node from finite-dimensional to infinite-dimensional chaotic systems. Based on the Lyapunov stability theory, we propose a general method to achieve the projective synchronization of time-delayed chaotic systems on random dynamical networks. We test its validity by investigating delay differential equations related to the optical bistable or hybrid optical device on Erdos-Renyi networks.