title: Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks.
abstract: We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.
authors.affiliation: Institute of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.
authors.forename: Cun-Fang
authors.initials: CF
authors.lastname: Feng
authors.forename: Xin-Jian
authors.initials: XJ
authors.lastname: Xu
authors.forename: Sheng-Jun
authors.initials: SJ
authors.lastname: Wang
authors.forename: Ying-Hai
authors.initials: YH
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D015233:Models, Statistical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010825:Physics / Q000379:methods*; D011897:Random Allocation; D013598:Systems Theory; D013995:Time; D013997:Time Factors