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.

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added.spatiotemporal chaos, sliding variable, parameter identification, synchronization, uncertain Gray-Scott system Spatiotemporal chaos synchronization has attracted much attention for its forefront theoretical study and practical application. Since Pecora and Carroll introduced a method to realize global synchronization between chaotic systems with the same structure in 1990 [1] , many methods and techniques for synchronization have been introduced, such as PC method, variable coupling method, adaptive control method, variable feedback method and so on [2][3][4][5][6][7][8][9][10][11][12][13][14] . The application of synchronization is rapidly extended from physics to information and communication, biology, chemistry, and many other fields. But most of the systems involved in the above methods are those with known parameters. While in reality, the parameters are always unstable or cannot be accurately determined in advance because of complex reasons of the system itself or limitation of technology in practical application. Therefore, linear coupling method was introduced by Lü et al. to realize chaos synchronization for Lorenz system, Chen systems, as well as Lü system with un-

In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time.

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In this paper, spherically symmetric structures of the Brusselator are calculated in detail by using the bifurcation theory. The results show that the solutions have both temporal-spacial dissipative-structures and a high coneentrative range in the centre of the sphere. These results will be greatly helpful in investigation of nuclear-type structures in biological and biochemical phenomena.