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A method is introduced to realize spatiotemporal chaos projective synchronization for a weighted network. The coupling function between connected nodes of the weighted network is derived and the range of the linear coefficient matrix of separated configuration in state equation of the node is obtained through constructing an appropriate Lyapunov function. Each node of the weight network is a laser spatiotemporal chaos model in which Bragg acousto-optical bistable system and unilateral coupled map lattices are taken as the local function and the spatial extended system, respectively. The projective synchronization effect of the weighted network is checked by numerical emulation. The results show that projective synchronization can be realized even if the coupling strength between the nodes are given arbitrary weight values.

Lag synchronization of spatiotemporal chaos in a weighted network with ring connection is studied in this paper. Spatiotemporal chaos systems are taken as the nodes of the network，and connections between the nodes are made through a weighted ring. According to stability theory，the condition to realize lag synchronization of the network is obtained by identifying the maximum Lyapunov exponent of the network. Lag synchronization exists in the whole network when the largest Lyapunov exponent is less than zero，and the coupling strength between the nodes can be given any weight value. Autocatalytic reaction-diffusion chaotic systems are taken as the nodes of the network，and simulation results show the effectiveness of the method.

A lag synchronization controller is designed to realize synchronization between spatiotemporal chaos systems. The structure of the lag synchronization controller and the error equations of state variables are determined based on Lyapunov stability theory. Autocatalytic reaction-diffusion chaotic system is taken as an example to verify the effectiveness of the controller. The parameter identifier is further designed to provide effective identification of the parameters in the uncertain autocatalytic reaction-diffusion chaotic system. The method is proved to have better performance in anti-jamming by studying the synchronizing effect under bounded noise.

The anti-synchronization of two nonlinear-coupled spatiotemporal chaotic systems is discussed. A special nonlinear-coupled term is constructed through suitably separating the spatiotemporal chaotic systems to linear and nonlinear terms, and anti-synchronization of two two-dimensional coupled map lattices is realized. The nonlinear-coupled method is further generalized to anti-synchronize the complex networks composed of two-dimensional coupled map lattices. The artificial simulation results show that this method is still effective.

A parameter observer is designed to identify Rossler system with unknow parameters. Chaos synchronization between uncertain Rossler system and Coullet system is realized via backstepping method.The synchronization controller is presented based on stability theory, and the area of controlling gain is determined. The simulation results show that all the state variables in the Coullet system can track any desired trajectory in the Rossler system exactly when the parameter observer and backstepping controller are functioning, which shows the method is effective and feasible.