Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control

A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.     

两个四维混沌系统广义投影同步

利用主动控制同步法设计合适的非线性反馈控制器，实现两个相同的四维混沌系统的同结构广义投影同步，以及实现两个不同的新型四维混沌系统异结构广义投影同步.通过改变广义投影同步的比例因子，获得任意比例于原驱动混沌系统输出的混沌信号.数值仿真表明了所设计的控制器有效性和理论推导的正确性.     

Inverse chaos synchronization between bidirectionally coupled variable multiple time delay systems

We make first report on inverse chaos synchronization between bidirectionally non-linearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model. The results are of certain importance in secure chaos-based communication systems.     

Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study

State tomography on qubit pairs is routinely carried out by measuring the two qubits separately, while one expects a higher efficiency from tomography with highly symmetric joint measurements of both qubits. Our numerical study of simulated experiments does not support such expectations.     

Inclined circular flat punch on a transversely isotropic piezoelectric half-space

Summary Utilizing the general solution of transversely isotropic piezoelectricity, the paper analyzes the problem of an inclined rigid circular flat punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to take into account the effect of the electric field in piezoelectric materials. Assuming that the punch is maintained at a constant electric potential, exact expressions for the elastoelectric field are derived in terms of elementary functions. It is noted that the solution corresponding to a flat circular punch centrally loaded by a concentrated force can be obtained as a special case. Received 15 December 1998; accepted for publication 9 March 1999     

Difference systems of sets and cyclotomy

Difference systems of sets (DSS) are combinatorial configurations that arise in connection with code synchronization. A method for the construction of DSS from partitions of cyclic difference sets was introduced in [V.D. Tonchev, Difference systems of sets and code synchronization, Rend. Sem. Mat. Messina, Ser. II, t. XXV 9 (2003) 217–226] and applied to cyclic difference sets (n,(n-1)/2,(n-3)/4) of Paley type, where is a prime number. This paper develops similar constructions for prime numbers that use partitions of the set of quadratic residues, as well as more general cyclotomic classes.     

L-拓扑空间中的相对强F紧性与相对超F紧性

In this paper,two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

外噪声作用下可激发系统中的预测同步现象

采用数值模拟方法研究了由2个完全相同的可激发系统,通过单向延迟反馈耦合连接所组成主动-从动系统中的预测同步现象.结果表明在相等的外噪声作用下,当延迟时间和耦合强度在适当的范围内取值时,从动系统发生放电活动时所产生的动作电位能够预测主动系统发生放电活动时所产生的动作电位,即出现了预测同步现象,并且预测时间不可能大于主动神经元的响应时间.     

A class of Sierpinski carpets with overlaps

Based on a scheme by Lau and Ngai, a sufficient and necessary condition for an IFS of contractive similitudes to satisfy the open set condition is given. A class of Sierpinski carpets with parameters (λ₁,λ₂) is then investigated.