Consistent Lyapunov exponent Estimation for one-dimensional dynamical systems

Summary  The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations.     

Critical exponents of discrete groups and -spectrum

Let be a noncompact semisimple Lie group and an arbitrary discrete, torsion-free subgroup of . Let be the bottom of the spectrum of the Laplace-Beltrami operator on the locally symmetric space , and let be the exponent of growth of . If has rank , then these quantities are related by a well-known formula due to Elstrodt, Patterson, Sullivan and Corlette. In this note we generalize that relation to the higher rank case by estimating from above and below by quadratic polynomials in . As an application we prove a rigiditiy property of lattices.

     

Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem

The following singular elliptic boundary value problem is studied:

     

Investigation of Hyperfine Interactions in CeIn3 byTDPAC

Magnetic hyperfine fields (mhf) at ¹¹¹Cd and ¹⁴⁰Ce nuclei, dilutely substituting the In and Ce sites, respectively, have been measured in the intermetallic compound CeIn₃ using perturbed angular correlation technique. A pure electric quadrupole interaction with an axially symmetric electric field gradient was observed at ¹¹¹In(EC)¹¹¹Cd probe nuclei at room temperature while a combined magnetic dipole and electric quadrupole interaction is observed below 10K. Below the ordering temperature, only a magnetic interaction is observed at ¹⁴⁰La(^–)¹⁴⁰Ce probe. The values of mhf measured experimentally as a function of temperature are discussed in terms of critical behavior.     

A Load-Balanced Network with Two Servers

A load-balanced network with two queues Q ₁ and Q ₂ is considered. Each queue receives a Poisson stream of customers at rate _i , i=1,2. In addition, a Poisson stream of rate arrives to the system; the customers from this stream join the shorter of two queues. After being served in the ith queue, i=1,2, customers leave the system with probability 1–p _i ^*, join the jth queue with probability p(i,j), j=1,2, and choose the shortest of two queues with probability p(i,{1,2}). We establish necessary and sufficient conditions for stability of the system.     

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.     

Temporal-spatial diversities of long-range correlation for relative humidity over China

Long-range correlations of daily relative humidity anomaly records from 191 weather stations over China during 1951-2000 are analyzed by means of fluctuation analysis (FA) and detrended fluctuation analysis (DFA). The information about trends in the relative humidity records can be obtained by comparing the FA curve with DFA curves. The daily relative humidity fluctuations are found to be power-law correlated and their average scaling exponent is higher than that of the temperature fluctuations, indicating that the relative humidity fluctuations take different statistical behavior from other meteorological quantities and there exists a stronger persistence in the relative humidity fluctuations. Furthermore, it is also found that these power-law scaling properties vary from station to station and show both spatial and temporal diversities, which may be explained by a proposed mechanism.     

Theoretical and experimental time series analysis of an inductorless Chua’s circuit

In this paper we have analyzed the time series obtained from an experimental realization of an inductorless version of Chua’s circuit. We have also compared the experimental results with the results emerging by analysis of the time series obtained by numerical simulations of the respective model equations. Lyapunov exponent spectra, the Kaplan-Yorke dimension and phase-space diagrams were used to show the similarities between theoretical and experimental results. We were able to identify the effects of the operational amplifier simulated inductor internal resistance on the Chua’s circuit dynamics. Decreasing internal resistance for decreasing current through the circuit was responsible for the observed bifurcation route.     

利用单模激光Lorenz系统实现混沌反控制

利用Lyapunov函数方法，对混沌反控制问题进行了研究.以单模激光Lorenz系统和描述心脏搏动的Bonhoeffer-Van der Pol系统为例，设计了一种控制器，成功地使Bonhoeffer-Van der Pol系统混沌化.给出了控制器的具体设计方案以及单模激光Lorenz系统与Bonhoeffer-Van der Pol系统状态之间误差系统的结构.仿真结果表明，在控制器的作用下，Bonhoeffer-Van der Pol系统所有状态变量严格地跟踪了单模激光Lorenz系统的混沌轨迹，对应的相空间中Bonhoeffer-Van der Pol系统的轨迹也由极限环转变为与单模激光Lorenz系统的轨迹完全相同的混沌吸引子，Bonhoeffer-Van der Pol系统严格地跟踪了单模激光Lorenz系统混沌的动态行为.     

Nonuniform stability properties and perturbing lyapunov functions

In this paper, without assuming the conditions everywhere, we study nonuniform stability properties of differential systems by employing the method of perturbing Lyapunov functions and splitting the given system suitably