Transmission time of a particle in the reflectionless Sech-squared potential: Quantum clock approach

We investigate the time for a particle to pass through the reflectionless Sech-squared potential. Using the Salecker-Wigner and Peres quantum clock an average transmission time of a Gaussian wave packet representing the particle is explicitly evaluated in terms of average momentum and travel distance. The average transmission time is shown to be shorter than the time of free-particle motion and very close to the classical time for wave packets with well-localized momentum states. Since the clock measures the duration of scattering process the average transmission time can be interpreted as the average dwell time.     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.     

Synchronization of different chaotic systems via active radial basis functions sliding mode controller

This paper presents a new method to synchronize different chaotic systems with disturbances via an active radial basis function （RBF） sliding controller. This method incorporates the advantages of active control, neural network and sliding mode control. The main part of the controller is given based on the output of the RBF neural networks and the weights of these single layer networks are tuned on-line based on the sliding mode reaching law. Only several radial basis functions are required for this controller which takes the sliding mode variable as the only input. The proposed controller can make the synchronization error converge to zero quickly and can overcome external disturbances. Analysis of the stability for the controller is carried out based on the Lyapunov stability theorem. Finally, five examples are given to illustrate the robustness and effectiveness of the proposed synchronization control strategy.     

Robust adaptive synchronization of chaotic neural networks by slide technique

In this paper, we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay. In order to increase the robustness of the two coupled neural networks, the key idea is that a sliding-mode-type controller is employed. Moreover, without the estimate values of the network unknown parameters taken as an updating object, a new updating object is introduced in the constructing of controller. Using the proposed controller, without any requirements for the boundedness, monotonicity and differentiability of activation functions, and symmetry of connections, the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are. Finally, the numerical simulation validates the effectiveness and feasibility of the proposed technique.     

Gradient control and synchronization of Julia sets

This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial Zn＋1 = zn^2＋ c, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.     

Breaking chaotic shift key communication via adaptive key identification

This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter's parameter (key). By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.     

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.     

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.     

复系统Julia集的同步

非线性系统中的分形集——Julia集, 在工程技术中有着十分重要的应用,定义了不同系统间的Julia集同步的概念, 并引入一种非线性耦合的方法, 对同一系统不同参数的Julia集进行了有效的同步.并以多项式形式和三角函数形式的Julia集同步为例验证了该方法的有效性.