Study On Issues Related To Chaos Synchronization

Firstly, a brief description of the chaos and synchronization is given. Then this dissertation mainly studies some issues related to chaos synchronization and proposes theoretical analysis, including the research on relation between noise and chaos synchronization, synchronization in complex dynamical networks, and synchronization of (discrete, non-autonomous, multi-scroll) chaotic systems. The work and contributions are summarized as follows:(1) Two aspects of relation between noise and chaos synchronization are studied. On the one hand, white noise with certain intensity is used as a feedback gain in order to achieve the purpose of generalized synchronization. The conditions required for noise coupling strength function are derived in detail. On the other hand, when chaotic systems are disturbed by noise, based on the robust control method, the feedback terms are designed for limiting the synchronization errors to a relatively small range. In addition, when the orders of driving-response systems are the same or not, two cases are considered and theoretical analysis gives sufficient conditions for synchronization.(2) Three aspects of synchronization in complex dynamical networks are studeid. First of all, synchronization of Chen systems in complex networks is invesrigated. Different with Lyapunov function method and linear approximation method, the approach proposed here can be used universally and ensure the monotonous synchronization. Consider four complex networks, including ring network, star network, small world network and globally coupled network, which all have N Chen systems, the sufficient conditions for synchronization are derived and the results are compared. Secondly, the impulsive pinning controlling method is applied to a small fraction of network nodes, in order that all nodes are synchronized to the equilibrium. The scheme designed here has universal applications and the cost for controlling is low. Finally, the existence of generalized synchronization in complex dynamical networks i s considered. G iven a specific n etwork, t he g eneralized s ynchronization c an be classified a ccording t o the status o f m odified s ystems. T heoretical p roofs a re p roposed to the existence and exponential attractive property of three types of generalized synchronization m anifold.(3) For discrete, non-autonomous and multi-scroll chaotic systems, the follows are studied: Firstly, synchronization of discrete chaotic systems with unknown parameters is researched. The controller and parameters are designed, and theoretical results prove that the method is effective. Secondly, because the synchronization manifold of non-autonomous chaotic systems is related to time, the mathematical mechanism of the synchronization is complicated. The g eneralized s ynchronization i s classified i nto f our t ypes a ccording t o the status o f m odified r esponse s ystems. T he c onditions f or the existence a nd exponential attractive p roperty o f three t ypes o f generalized s ynchronization m anifold a re g iven, and H?lder continuity induced by the non-smooth synchronized manifold is considered. Finally, taking a specific multi-scroll chaotic system for illustration, the phenomenon of multi-stable chaotic attractors in generalized synchronization is discussed. It is found that in response system, there exist multi-stable chaotic attractors, which all synchronize with the driving system. Moreover, which attractor the response system arrives depends on the coupling parameters and initial conditions.For all the above problems, numerical simulations are proposed, which verify the corresponding theoretical results.