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This paper studies global synchronization between a heterogeneous dynamical network and a known target trajectory via distributed impulsive control. Synchronization with an error level, called quasi-synchronization, is analyzed by utilizing the time-varying Lyapunov function. Some sufficient quasi-synchronization conditions are presented and explicit expressions of error levels are derived. Furthermore,...
In this paper, the impulsive control problem on the synchronization for a class of chaotic systems is discussed. Based on Lyapunov stability theory, the new impulsive synchronization strategy is presented to realize the chaos synchronization and possesses the wider scope of application. Finally the numerical simulation examples are given to demonstrate the effectiveness of our theoretical results.
This paper studies the problem of synchronization on a complex dynamical network where the nodes' dynamics are nonlinear time-invariant systems and share a directed communication network. Firstly, we study the problem of synchronization on a directed network with physical links. An explicit Lyapunov function is constructed by using an appropriate matrix to derive the threshold of event generator....
Generalized projective synchronization (GPS) of chaotic systems is a new type of synchronization, which is a general form of synchronization compared to other types of synchronization such as complete synchronization (CS), anti-synchronization (AS), hybrid synchronization (HS), projective synchronization (PS), etc. There are many types of techniques available for synchronizing chaotic systems such...
Based on the Lyapunov stability theory and fractional-order stability theory, the disorder projective synchronization for four-dimension fractional-order Modified Chua's system is successfully investigated by a nonlinear controller. Meanwhile, the error variables approach gradually to zero with time and the time-history of different variables satisfied the scaling factors. In addition, numerical simulations...
In this paper, we study synchronization of a dynamical network whose nodes are linear time-invariant systems and are interconnected through a shared communication network. Firstly, synchronization of a dynamical network with physical links and undirected topology is reinvestigated from a set stability point of view. An explicit Lyapunov function with respect to its synchronization manifold is constructed...
This paper is concerned with the ultimate bounds and positively invariant sets for a system describing the amplitude of a plasma instability proposed by Pikovski, Rabinovich and Trakhtengerts. Based on generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive a new ellipsoidal estimate and a cylindrical domain of the globally exponentially...
This paper investigates the synchronization of fractional-order chaotic systems via sliding mode control method. A fractional-order sliding surface is proposed and the corrreponding controller is formulated based on the fractional version of the Lyapunov stability theory, which can guarantees asymptotical stability of fractional-order chaotic systems. Finally, simulation results are given to demonstrate...
The synchronization problem between two nonidentical complex networks with time delay coupling is studied in this paper, which also considered the noises in the transmission channel. Two kinds of complex dynamical networks including coupled with states and coupled with outputs are studied. The synchronization controllers are designed by using the integral control approach to suppress the effect introduced...
In this paper, the synchronization of fractional- order hyperchaotic Lorenz system is investigated. Based on a time-domain method and the Lyapunov stability theory, the synchronization problem of the fractional-order system can be converted into an equivalent problem of stabilizing the integer-order system. Numerical simulations are used to illustrate the effectiveness of the proposed synchronization...
In this paper, adaptive control approach with uncertain parameters or not for 2D discrete-time Ushiki system is discussed both theoretically and numerically. Based on the Lyapunov stability theorem and the chaotic controlling methods, adaptive control scheme with uncertain parameters or not is given and illustrated with Ushiki system as example. Numerical simulations are presented to demonstrate the...
A new chaotic system, which is three-mode truncation of Couette-Taylor flow, is discussed. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via Lyapunov function. Feedback control and adaptive control methods are used to achieve the globally exponentially synchronization. Numerical simulation results show the effectiveness of these methods.
This paper treats chaos anti-synchronization between Liu system and Rössler system with unknown parameters via adaptive control. Based on Lyapunov stability theory, the adaptive control law and the parameter update rule for unknown parameters are derived to ensure the anti-synchronization of the two non-identical chaotic systems. Numerical simulations are also shown to verify the results.
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