Chaotic jets with multifractal space-time random walk

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.     

Chaotic layer of a pendulum under low-and medium-frequency perturbations

The amplitude of the separatrix map and the size of a pendulum chaotic layer are studied numerically and analytically as functions of the adiabaticity parameter at low and medium perturbation frequencies. Good agreement between the theory and numerical experiment is found at low frequencies. In the medium-frequency range, the efficiency of using resonance invariants of separatrix mapping is high. Taken together with the known high-frequency asymptotics, the results obtained in this work reconstruct the chaotic layer pattern throughout the perturbation frequency range.     

The contribution of asymptotics to combustion

After a brief historical review of combustion science, the role of asymptotics is elucidated by a discussion of the hydrodynamical limit, the small Mach number approximation, Damkohler number asymptotics, and activation energy asymptotics. The importance of the latter is emphasized by examining its application to flame propagation, stability, explosions, and diffusion flames.     

一种新型的双向长距离光纤混沌保密 通信系统性能研究

基于两个在驱动混沌信号注入下的响应半导体激光器之间的混沌同步, 提出了一种新型的可实现信息双向、长距离保密传输的系统, 并建立了相应的理论模型. 利用该理论模型, 研究了系统的双向传输性能、 安全性能以及系统性能随传输距离的变化. 结果表明: 两个响应激光器在受到发自同一驱动混沌激光器的混沌光注入下, 其混沌输出虽然与注入混沌信号相差很大, 但两个响应激光器的混沌输出却能实现非常好的无时间延迟的等时同步; 对窃听者可能获取信息的各个途径进行了考察, 结果显示该系统具有很好的安全性; 采用普通单模光纤作为传输信道, 信息经过50 km传输后, 解调信息Q因子可达到6以上; 采用色散位移光纤, 信息经过200 km的传输, 解调信息Q因子还可达6以上.     

混沌信号在光纤传输过程中的非线性演化

对光纤混沌传输理论及混沌信号与光纤传输媒介相互作用的物理机制进行了理论研究. 通过耦合激光混沌系统和光纤传输信道，提出光纤混沌信号传输的非线性演化物理模型. 着重分析光纤自相位调制对激光混沌信号传输与演化的作用. 结果表明：自相位调制不影响混沌信号脉冲的形状，但能产生非线性相移使混沌信号频谱展宽；自相位调制不影响混沌信号脉冲的功率分布和场强分布，但能影响混沌信号脉冲的功率频谱分布，影响混沌信号光场以及慢变场的变化. 提出混沌信号在光纤传输中的非线性演化频率啁啾和形式，数值模拟了混沌信号在光纤传输过程中的相位、频谱、场以及场的慢变部分的相空间等演化形式和特点. 关键词： 混沌 光纤 传输 演化     

Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias

The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.     

Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems

We study a phenomenon of noise-induced intermittency for the stochastically forced one-dimensional discrete-time system near tangent bifurcation. In a subcritical zone, where the deterministic system has a single stable equilibrium, even small noises generate large-amplitude chaotic oscillations and intermittency. We show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium. For the analysis of this system, we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique. An explicit formula for the value of the noise intensity threshold corresponding to the onset of noise-induced intermittency is found. On the basis of our approach, a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given.     

Statistical properties of passive scalar in a random flow with a strong shear component

We study mixing of passive scalar by a chaotic velocity field with a relatively strong regular shear component. We show that the tail of partition distribution function (PDF) of coarse-grained passive scalar field differs qualitatively from the corresponding asymptotics in the case of isotropic flow statistics.     

混沌光学系统辨识的支持向量机方法

将支持向量机用于混沌光学系统的辨识,以布拉格声光双稳混沌系统为例,通过计算机仿真实验,尝试了用最小二乘支持向量机进行混沌光学系统辨识的可行性,并将其与采用反向传播算法的前向神经网络辨识方法进行了比较。采用最小二乘支持向量机辨识的优点是其训练过程遵循结构风险最小化原则,不易发生过拟合现象;它通过解一组线性方程组可得到全局唯一的最优解;最小二乘支持向量机的拓扑结构在训练结束时自动获得而不需要预先确定。结果表明,本方法的辨识精度和速度均优于基于反向传播算法的前向神经网络,且对含噪混沌光学系统的辨识也同样适用,它可作为混沌光学系统辨识的有力工具。     

Clustering of Periodic Orbits and Ensembles of Truncated Unitary Matrices

In present article we consider a combinatorial problem of counting and classification of periodic orbits in dynamical systems on an example of the baker’s map. Periodic orbits of a chaotic system can be organized into a set of clusters, where orbits from a given cluster traverse approximately the same points of the phase space but in a different time-order. We show that counting of cluster sizes in the baker’s map can be turned into a spectral problem for matrices from truncated unitary ensemble (TrUE). We formulate a conjecture of universality of the spectral edge in the eigenvalues distribution of TrUE and utilize it to derive asymptotics of the second moment of cluster distribution in the regime when both the orbit lengths and the parameter controlling closeness of the orbit actions tend to infinity. The result obtained allows to estimate the size of average cluster for various numbers of encounters in periodic orbit.     

Sensitivity of ray travel times

Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.     

Effect of transmission fiber and amplifier noise on optical chaos synchronization

Optical chaos propagation has few constraints peculiar to itself which do not become as significant in conventional nonchaotic optical communication. We have investigated the effects of transmission fiber nonlinearities, dispersion and noise of erbium doped fiber amplifier (EDFA) on chaotic signal synchronization in lumped and distributed configuration. It is found that the effects of fiber dispersion can be easily compensated; however, the effects of fiber nonlinearity on chaos cannot be overdone and must be avoided. Three distinct configurations with different combinations of standard telecommunication fiber, dispersion compensation fiber and lumped and distributed EDF for amplification are analysed. The results are compared in terms of sync diagrams and noise figure. The chaos after propagation through distributed amplification performs better as compared to lumped amplification. Also, a new quantitative measure for the calculation of deviation in sync diagram of chaos is introduced.     

Ordered bursting synchronization and complex wave propagation in a ring neuronal network

Ordered bursting synchronization and complex propagation are investigated for a ring neuronal network in which each neuron exhibits chaotic bursting behaviour. The neurons become more and more synchronous in chaotic bursting as the synaptic strength is increased. It is shown that excitatory chemical synapses can effectively tame the chaos, and ordered bursting synchronization can be observed as the synaptic strength is further increased. However, synchronization among neurons is weakened as the number of neurons is increased. More importantly, it is shown that ordered bursting synchronization can be turned into spiking synchronization at certain noise intensity. Complex spatio-temporal patterns propagating towards both sides of pacemaker are found in this network before the emergence of spiking synchronization.     

Propagation of longitudinal waves in a random binary rod

Propagation of waves in a composite elastic rod consisting of rods with alternating properties of random length is considered. We calculate exactly the Lyapunov exponent and find its short and long wave asymptotics. Finally, we discuss conditions for propagation and localization of waves in a binary random medium.     

Bifurcation cascade as chaotic itinerancy with multiple time scales

A coupled chaotic system with a variety of time scales is studied. Under a certain condition, it is shown that a change in fast dynamics can influence slow dynamics with a huge time-scale difference, successively through propagation of correlation over elements. This propagation is given by bifurcation cascade, for which three conditions are found to be essential: strong correlation, bifurcation of fast element dynamics by the change of its parameter, and marginal stability. By using coupled Lorenz equation with multiple time scales, it is shown that chaotic itinerancy (CI) observed there leads for the system to satisfy the three conditions, and the bifurcation cascade occurs. Through the analysis of the CI, characteristic properties of the bifurcation cascade, asymmetry in propagation with regards to the time scale, and the universality of the results are discussed, with possible relevance to biological memory.     

Propagation of longitudinal waves in a random binary rod

Propagation of waves in a composite elastic rod consisting of rods with alternating properties of random length is considered. We calculate exactly the Lyapunov exponent and find its short and long wave asymptotics. Finally, we discuss conditions for propagation and localization of waves in a binary random medium.     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

Acoustic analog of the Fermi resonance

It is shown that for acoustic waves in crystals nonlinear phenomena of a new type, analogous to some degree to Fermi resonance in molecules, can occur. It is demonstrated on the basis of an analysis of the numerical solution of the equations of motion that for propagation of waves with different polarization and with sound velocities in integral ratio, the energy transfer from one wave to another is of the nature of beats with quite low amplitudes and can become chaotic as the amplitudes increase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 417–422 (25 March 1999)     

Synchronization and propagation of bursts in networks of coupled map neurons

The present paper studies regular and complex spatiotemporal behaviors in networks of coupled map-based bursting oscillators. In-phase and antiphase synchronization of bursts are studied, explaining their underlying mechanisms in order to determine how network parameters separate them. Conditions for emergent bursting in the coupled system are derived from our analysis. In the region of emergence, patterns of chaotic transitions between synchronization and propagation of bursts are found. We show that they consist of transient standing and rotating waves induced by symmetry-breaking bifurcations, and can be viewed as a manifestation of the phenomenon of chaotic itinerancy.     

Complex dynamics of a distributed parametric oscillator

The dynamics of a system with three parametrically coupled waves with delayed feedback is considered. Results of the detailed numerical simulation of the onset of self-modulation, as well as complex dynamic and chaotic regimes, are presented. The relation of self-modulation regimes with the formation and propagation of solitons is investigated. It is discovered that as the pump parameter increases, the synchronization of phases of the interacting waves, which is characteristic of stationary generation and periodic self-modulation regimes, is violated, and the system goes to a chaotic regime via intermittency.