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.     

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.     

混沌信号发生器

本给出一种用普通的电阻、电容和运算放大器实现的非自治混沌信号发生器电路。适用于进行混沌理论的演示实验教学。     

Chen混沌系统的非线性全局同步控制

研究了Chen提出的一个新的混沌系统的混沌同步问题,利用非线性控制方法设计了三种混沌同步控制器,并用李雅普诺夫方法证明了在混沌控制器作用下,驱动、响应混沌系统可以实现全局同步.数值仿真结果表明,所设计的三种混沌控制器都能有效的实现混沌同步,并且具有很强的鲁棒性.     

Experimental and numerical investigations on the pure material instability of an Oldroyd's 3-constant model

Received March 25, 2001 / Published online November 15, 2001     

Image Encryption Scheme with Compressed Sensing Based on a New Six-Dimensional Non-Degenerate Discrete Hyperchaotic System and Plaintext-Related Scrambling

Digital images can be large in size and contain sensitive information that needs protection. Compression using compressed sensing performs well, but the measurement matrix directly affects the signal compression and reconstruction performance. The good cryptographic characteristics of chaotic systems mean that using one to construct the measurement matrix has obvious advantages. However, existing low-dimensional chaotic systems have low complexity and generate sequences with poor randomness. Hence, a new six-dimensional non-degenerate discrete hyperchaotic system with six positive Lyapunov exponents is proposed in this paper. Using this chaotic system to design the measurement matrix can improve the performance of image compression and reconstruction. Because image encryption using compressed sensing cannot resist known- and chosen-plaintext attacks, the chaotic system proposed in this paper is introduced into the compressed sensing encryption framework. A scrambling algorithm and two-way diffusion algorithm for the plaintext are used to encrypt the measured value matrix. The security of the encryption system is further improved by generating the SHA-256 value of the original image to calculate the initial conditions of the chaotic map. A simulation and performance analysis shows that the proposed image compression-encryption scheme has high compression and reconstruction performance and the ability to resist known- and chosen-plaintext attacks.     

Modeling of cascaded high isolation bidirectional amplification in long-distance fiber-optic time and frequency synchronization system

We propose a physical model of estimating noise and asymmetry brought by high isolation Bi-directional erbiumdoped fiber amplifiers(Bi-EDFAs), no spontaneous lasing even with high gain, in longdistance fiber-optic time and frequency(T/F) synchronization system. It is found that the Rayleigh scattering noise can be suppressed due to the high isolation design, but the amplified spontaneous emission(ASE) noise generated by the high isolation Bi-EDFA and the bidirectional asymmetry of the transmission link caused by the high isolation Bi-EDFA will deteriorate the stability of the system.The calculated results show that under the influence of ASE noise, the frequency instability of a 1200 km system composed of 15 high isolation Bi-EDFAs is 1.773 × 10-13/1 s. And the instability caused by asymmetry is 2.6064 × 10-16/30000–35000 s if the total asymmetric length of the bidirectional link length is 30 m. The intensity noises originating from the laser and detector, the transfer delay fluctuations caused by the variation in ambient temperature and the jitter in laser output wavelength are also studied. The experiment composed of three high isolation Bi-EDFAs is done to confirm the theoretical analysis. In summary, the paper shows that the short-term instability of the T/F synchronization system composed of high isolation Bi-EDFAs is limited by the accumulation of ASE noise of amplifiers and the laser frequency drift, while the long-term instability is limited by the periodic variation in ambient temperature and the asymmetry of the amplifiers.The research results are useful for pointing out the direction to improve the stability of the fiber-optic T/F synchronization system.     

Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency

The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.