Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

Detecting positive feedback in multivariate time series: The case of metal prices and US inflation

The objective of this paper is to examine causality and feedback relationships between primary commodity prices and US inflation. To this end, the bivariate noisy Mackey–Glass process recently developed by Kyrtsou and Labys [Evidence for chaotic dependence between US inflation and commodity prices, J. Macroecon. 28(1) (2006) 256–266] has been applied to assess this relationship. Results obtained support evidence in favour of causality, which can help to identify the influences of speculative price behaviour on inflation.     

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.     

Finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay via periodically intermittent control

In this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 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.     

Synchronization in a Mutualism Ecosystem Induced by Noise Correlation

Understanding the cause of the synchronization of population evolution is an important issue for ecological improvement. Here we present a Lotka-Volterra-type model driven by two correlated environmental noises and show, via theoretical analysis and direct simulation, that noise correlation can induce a synchronization of the mutualists. The time series of mutual species exhibit a chaotic-like fluctuation, which is independent of the noise correlation, however, the chaotic fluctuation of mutual species ratio decreases with the noise correlation. A quantitative parameter defined for characterizing chaotic fluctuation provides a good approach to measure when the complete synchronization happens.     

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.