Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.     

分数阶混沌系统与整数阶混沌系统之间的同步

基于追踪控制的思想,利用分数阶系统稳定性理论,实现了分数阶混沌系统与整数阶混沌系统之间的混沌同步,给出了补偿器和反馈控制器的选择方法. 以三维分数阶Chen系统和三维整数阶Lorenz混沌系统之间的混沌同步为例进行了数值仿真和电路仿真. 研究表明了该同步方法的有效性.     

Traveling wavefront ray tracing and its applications

The current discussion of whether marine geodesy is something entirely new or part of oceanography or geodesy can be clarified by re‐examining our notions about the basic business of geodesy. This paper contends that the same basic geodetic services, which were needed for millenia to chart and control new territory, are being adapted now to the marine environment to suit modern accuracy standards. In a brief historical review it is shown that conceptually, the oceanic regions were always an integral part of geodetic concern. The oceans were certainly part of the world for the ancient map makers and for Pythagoras’ spherical earth model. Notions connected with the marine geoid were implied in ancient speculations. Distances and directions at sea, even depths, were determined to meet the requirements of the times. With the modern sophistication in geodetic theory and measuring techniques, these ideas became more refined and demanding in turn, but they were there all the time. For obvious reasons, land geodesy developed faster; marine geodesy will catch up now, because only now there is the technical capability and also an urgent economic motivation.     

不确定混沌系统的反同步与参数辨识

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.     

Modeling of volume reverberation in the ray approximation

We propose a numerical model for the evaluation of the three-dimensional scattering of sound in the sea. The model is based on the construction of ray patterns both for the primary and secondary (scattered) radiation. The intensity of secondary radiation is expressed via the coefficient of backward volume scattering interpreted as the fraction of backward-scattered acoustic energy per unit length of the primary ray. It is shown that, in the first approximation, it suffices to consider the secondary rays repeating the paths of the primary rays in the opposite direction. The attenuation of the intensity of sound along the paths of the primary and secondary rays is taken into account. The results of numerical analysis of the reverberation signal as a function of time are presented for various conditions (different depths of immersion of the antenna and widths of the directional diagram and the presence of sound-scattering layers). The proposed approach can be used for the purposes of modeling of the surface and bottom reverberation and for the solution of the inverse problems of underwater acoustics. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 50–58, September–October, 2007.     

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.     

Sensitivity analysis of the climate of a chaotic system

This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational ("adjoint") sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the "macroscopic climate sensitivity"(that is, the sensitivity of time‐averaged properties of the system to finite‐amplitude perturbations). This problem occurs even for time‐averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble‐adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter‐combinations to be explored further through direct finite‐amplitude perturbations.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

A study of hybrid and chaotic long-range propagation in a doublesound channel environment

This paper presents the results of the analysis of long range propagation (~200 km) in a range-dependent environment. The propagation medium is characterized by two deep sound channels. The range dependence enables energy transfer between the channels and leads to a mismatch between real data and ray predictions. To explain this mismatch, an analysis of hybrid ray propagation is presented. This analysis is completed by an interpretation in terms of chaos. This chaos is quantified in the particular case of the Bay of Biscay environment. This paper puts forward that mesoscale perturbations, such as the Mediterranean outflow in the North Atlantic, can affect long-range propagation. However, it shows that the ray theory remains reliable for a propagation range of several hundred kilometers     

The effects of chaotic advection in a three-layer ocean model

A three-layer model of an inviscid incompressible fluid is considered in a quasigeostrophic approximation within the concept of background currents. A singular topographic obstacle yields the formation of a vortical motion in the layers. It is always present in the lower layer, while in the upper and middle layers it can be observed only at certain velocities of the external flows. Three current functions describing a singular topographic flow in the lower layer and two regular flows in the upper layer are obtained. In case of a nonstationary harmonic perturbation of the external flow, chaotic particle transport is possible in these flows. This paper analyzes the chaotic properties of this model. Depending on the type of unperturbed frequency curves of the fluid particle revolution is determined by the model parameters (stratification) and the incident flow, the patterns of the chaotic transport will substantially differ. Two of the limiting dependences of the revolution frequency are determined, namely, the dependence for a singular vortex and that for a regular vortex with the smallest area. Other dependences are intermediate ones. Two limiting types of revolution frequencies determine the two different scenarios of chaotic advection.     

Propagation and trapping of inertial gravity waves in shear flows (ray theory)

The process of propagation and trapping of inertial gravity wave (IGW) packets in oceanic shear flows is studied in the geometric-optics approximation (ray theory). It is shown that wave trapping in strong stable stratification occurs in the region of anticyclonic (horizontal) velocity shear in a narrow frequency range on the left side of the inertial frequency. Beyond this range, the packet (ray) is either reflected from a cyclonic shear layer or propagates freely through the shear layer. The basic equations of ray theory are analyzed qualitatively, and analytical expressions are derived for freely propagating and trapped rays. The influence that vertical shear exerts on the ray behavior is also investigated. It is shown that two-dimensional ray focusing occurs as the velocity profile decreases with depth, so that rays concentrate along a specific latitude.     

The RRA algorithm: recursive ray acoustics for three-dimensionalspeeds of sound

A recursive ray acoustics (RRA) algorithm for three-dimensional speeds of sound is presented. The RRA algorithm is simple, fast, and accurate and uses arc length as the independent variable. In its present form, it can be used to compute the position, angles of propagation, travel time, and path length along a ray path. Preliminary results from computer simulation studies designed to test the algorithm's accuracy and capabilities are also presented     

Complex dynamics and chaotic responses in the time domain simulations of a floating structure

The motion of a moored semi-submersible is modelled using a semi-empirical nonlinear ordinary differential equation. Time domain simulations, guided by the qualitative theory of dynamical systems, illustrate the extremely complex nature of typical responses in regular seas. The importance of nonlinearities is emphasised together with the implications for floating structures in general.     

采样间隔和插值对混沌系统可预报期限估计的影响

利用非线性局部Lyapunov指数的方法研究了采样间隔和插值对混沌系统可预报性的影响,结果表明:在一定范围内,采样间隔对系统可预报期限估计的影响基本是随采样间隔的增大而逐渐减小。但当采样间隔超过一定大小时,所得序列已不能找到真实的局地动力相似,无法得到其真实的误差增长情况,也无法得到系统准确的可预报期限的估计。本文通过插值的方法试图还原同样长度的时间序列,结果表明不论是在采样间隔较大还是较小的情况下,插值都不能有效地改善对系统可预报期限的估计。此外,在采样间隔固定的情况下,随着插值个数的增多,系统的可预报期限的估计反而更低。以上结果提示我们在利用实际海洋观测资料估计其可预报期限时,选用较高分辨率较长时间序列的资料可以得到更接近真实的可预报期限。     

The frequency and effect of shark-inflicted bite injuries to the reef manta ray Manta alfredi

Shark bite injuries on reef manta rays Manta alfredi off the coast of Inhambane, Mozambique, were examined over a three-year period (2003–2006). The frequency and seasonality of attacks, the rate of wound healing, and the possible identities of attackers were explored. This study presents the first examination of bite wounds on manta rays in the wild and the role sharks may play in the natural mortality of this species. The reported incidence of shark-inflicted injuries is high with over three-quarters of the sampled population affected. In total, 571 bite injuries were observed on 283 identified individuals. The number of bite injuries varied from one to seven, with a mean of 1.54 bite wounds. There was no significant difference in the frequency of bite injuries in male and female rays. The majority (96%) of the observed bite wounds were healed. Fresh wounds occurred throughout the year, with no obvious seasonality. The bull shark Carcharhinus leucas and tiger shark Galeocerdo cuvier are suggested as the primary mediators of attacks, although up to 11 other shark species are listed as potential attackers. The majority of the bite marks (96%) occurred to the most posterior region of the body, specifically the posterior edges of the pectoral and pelvic fins, with many injuries likely having a negative impact on the reproductive abilities and fitness of the rays.     

Ridge and swale topography of the Middle Atlantic Bight,Nnorth America: Secular response to the Holocene hydraulic regime

The ridge and swale topography of the Middle Atlantic Bight was originally interpreted as a relict strand plain whose ridges reflect stillstands of the returning Holocene sea. However, close examination indicates that the ridges appear to be instead longitudinal bed forms, responses to a regime of intermittent, south-trending storm currents. Ridges may be initiated on the shore face and detached as the coast retreats to form fields of isolated ridges, or they may be molded into the shelf-transverse sand massifs that mark the retreat paths of littoral-drift depositional centers at estuary mouths and off cuspate forelands. The ridge and swale topography is thus a stable end configuration toward which a variety of near-shore constructional topographies have converged during the Holocene transgression.Morphologic evidence for readjustment of ridge topography to the deepening shelf flow field during the Holocene transgression is discernable. However, the extent to which the offshore topography continues to respond to hydraulic regime is unclear. The role of helical flow structure in the storm flow field remains to be documented. Resolution of these problems will require more detailed information of hydraulic process and substrate response on storm-dominated shelves.     

空间电荷效应对X射线条纹相机动态范围影响的研究

在惯性约束聚变中,X射线条纹相机是一种诊断图像时空分辨的重要设备,其动态范围反映了条纹相机有效测量入射X射线强度的能力.由于空间电荷效应的存在,电子脉冲在运动过程中会不断展宽,从而限制了条纹相机的动态范围.本文采用一维流体力学模型,利用电子数守恒、动量守恒和Poisson方程等来对电子脉冲的展宽进行推导,最终得到了电子脉冲的密度分布随时间空间的变化情况,从而为条纹相机动态范围的评估提供了依据.