Finite-time signal lag-projective synchronous transmission between uncertain complex networks with NH3 and CO2 lasers

The finite-time signal lag-projective synchronous transmission problem of two uncertain complex networks with NH₃ and CO₂ lasers is investigated. First, the chaotic characteristics of NH₃ laser and CO₂ laser are derived. Then two networks with unknown parameters and uncertain topological structure are constructed. Based on the finite-time stability theory and LaSalle's principle, the effective synchronous transmission controller and corresponding update laws are designed to guarantee lag-projective synchronization of the two uncertain complex networks in a given finite-time. Simultaneously, the unknown parameters of node dynamic are estimated successfully and the uncertain topology weights tend to the proper constants. Finally, the NH₃ laser and CO₂ laser are taken as node dynamics to constitute drive-response networks for simulation. The simulation results verified the effectiveness of the synchronization criteria. Moreover, the proposed approach can rapidly track the network topology changes well and the weight topology structure values are automatically adapted to the appropriate constants in the process of synchronous transmission. Furthermore, the proposed method is universal which need not assume the node dynamics satisfy the powerful and conservative Lipchitz condition.