Dynamics in two-elevator traffic system with real-time information

We study the dynamics of traffic system with two elevators using a elevator choice scenario. The two-elevator traffic system with real-time information is similar to the two-route vehicular traffic system. The dynamics of two-elevator traffic system is described by the two-dimensional nonlinear map. An elevator runs a neck-and-neck race with another elevator. The motion of two elevators displays such a complex behavior as quasi-periodic one. The return map of two-dimensional map shows a piecewise map.     

一维保守系统的周期运动与周期-能量关系

对于由哈密顿函数H(p，q)描述的一维保守系统，导出了当等能线是绕中心的闭合曲线时，相点始终按顺时针或逆时针方向运动的条件，以及振动的周期与系统的能量之间的关系式，讨论了质点在对称势阱内作周期运动的一类情况，并把谐振子、“x^n振子”、单摆及Duffing振子(硬非线性弹簧与软非线性弹簧)作为应用实例。     

Dynamics analysis of a 5-dimensional hyperchaotic system with conservative flows under perturbation

Conservative chaotic flows have better ergodicity, therefore researching dynamics and applications of conservative systems has become a hot topic. We introduce a constant-perturbation into a 5-dimensional(5D) conservative model.Consequently, the line equilibria of original model have been changed to non-equilibrium. Plentiful chaos phenomena such as coexisting conservative flows can be observed in this modified system. In addition, by increasing the magnitude of the disturbance, the conservative system can be transformed to a dissipative system. Then, the modified system is realized by an xc7z020clg400 field programmable gate array(FPGA) chip. The designed chaotic oscillator consumes fewer resources and has high iteration speed. Finally, a pseudo random number generator based on this novel digital oscillator is designed.     

推广的一类Lie代数及其相关的一族可积系统

对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便，本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数，通过对阶数的规定，得到了一类新的loop代数.作为其应用，设计了一个新的等谱问题，得到了一个新的Lax对.利用屠格式获得了一族新的可积系统，具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形，得到了新的耦合广义Schrdinger方程. 关键词： Lie代数 可积系 Hamilton结构     

Effect of Environment on Photo-detachment Dynamics of Halide Ions: A Model Approach

利用外部光场,采用二维模型的方法研究了闭壳阴离子系统在极性溶剂环境介质中光解动力学过程．同时用一个简单的模型研究了系统中溶剂极化和外界电荷之间强耦效应．卤离子的电子态用二维模型哈密尔顿函数表示,采用含时傅立叶格点哈密顿方法研究解离过程．通过上述两种不同的方法揭示溶剂环境对光解动力学的影响：引入影响阴离子系统能量的极性溶剂来改变有效势能面和利用井深的随机波动来模拟系统．另外对作为光场重要参数的光解平均速率常数进行计算,定性地解释了溶剂效应对于偶极束缚阴离子系统的影响．     

广义Hamilton系统的Lie对称性与守恒量

研究广义Hamilton系统Lie对称性导致的新型守恒量.首先,建立系统的微分方程.其次,研究一类特殊无限小变换下系统的Lie对称性.第三,将Hojman定理推广到广义Hamilton系统.最后,举例说明结果的应用. 关键词： 广义Hamilton系统 Lie对称性 守恒量     

Finite Range of Large Perturbations in Hamiltonian Dynamics

The dynamics defined by the Hamiltonian , where the _m are fixed random phases, is investigated for large values of A, and for . For a given P ^* and for , this Hamiltonian is transformed through a rigorous perturbative treatment into a Hamiltonian where the sum of all the nonresonant terms, having a Q dependence of the kind cos(kQ – nt + _m) with \Delta \upsilon$$ " align="middle" border="0"> , is a random variable whose r.m.s. with respect to the _m is exponentially small in the parameter . Using this result, a rationale is provided showing that the statistical properties of the dynamics defined by H, and of the reduced dynamics including at each time t only the terms in H such that , can be made arbitrarily close by increasing . For practical purposes close to 5 is enough, as confirmed numerically. The reduced dynamics being nondeterministic, it is thus analytically shown, without using the random-phase approximation, that the statistical properties of a chaotic Hamiltonian dynamics can be made arbitrarily close to that of a stochastic dynamics. An appropriate rescaling of momentum and time shows that the statistical properties of the dynamics defined by H can be considered as independent of A, on a finite time interval, for A large. The way these results could generalize to a wider class of Hamiltonians is indicated.     

Dynamics of fluctuations in a reactive system of low spatial dimension

We study, using master equation techniques, the time evolution of the average concentration and fluctuations in the two-speciesn-molecule reactionA+(n-1)XnX in one dimension described by a Glauber-type dynamical lattice model for the specific casesn=2 (bimolecular) andn=3 (trimolecular). The evolution is found to be quite different from that described by the Mean-Field equations even for the bimolecular case, where the steady state is meanfield. For the trimolecular process, the values of fluctuation correlations in the nonequilibrium steady state are well predicted by the fixed points of the dynamical equations obtained from the master equation. In addition, three-point fluctuation correlations are found to play an important role in both processes and are accounted for by an extended Bethe-type ansatz. The bimolecular system shows no memory effects of initial conditions, while the trimolecular system is characterized by memory effects in terms of the average concentration, fluctuations as well as the entropy. The spatial decay of fluctuation correlations is found to be short range at the steady state for the trimolecular system.     

Dynamics analysis in a tumor-immune system with chemotherapy

An ordinary differential equation (ODE) model of tumor growth with the effect of tumor-immune interaction and chemotherapeutic drug is presented and studied. By analyzing the existence and stability of equilibrium points, the dynamic behavior of the system is discussed elaborately. The chaotic dynamics can be obtained in our model by equilibria analysis, which show the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, the action of the infusion rate of the chemotherapeutic drug on the resulting dynamics is investigated, which suggests that the application of chemotherapeutic drug can effectively control tumor growth. However, in the case of high-dose chemotherapeutic drug, chemotherapy-induced effector immune cells damage seriously, which may cause treatment failure.     

关于Lagrange系统和Hamilton系统的Mei对称性

对Lagrange 系统和Hamilton系统Mei对称性的研究表明，Mei对称性的两种表述对Lagrange系统是等价的，给出一类Mei对称性，而对Hamilton系统不等价，给出两类Mei对称性. 关键词： Lagrange系统 Hamilton系统 Mei对称性 守恒量     

Transition to chaos in the conservative four-wave parametric interactions

In this work, we analyze the transition from regular to chaotic states in the parametric four-wave interactions. The temporal evolution describing the coupling of two sets of three-waves with quadratic nonlinearity is considered. This system is shown to undergo a chaotic transition via the separatrix chaos scenario, where a soliton-like solution (separatrix) that is found for the integrable (perfect matched) case becomes irregular as a small mismatch is turned on. As the mismatch is increased the separatrix chaotic layer spreads along the phase space, eventually engrossing most part of it. This scenario is typical of low-dimensional Hamiltonian systems.     

Equipartition thresholds in chains of anharmonic oscillators

We perform a detailed numerical study of the transition to equipartition in the Fermi-Pasta-Ulam quartic model and in a class of potentials of given symmetry using the normalized spectral entropy as a probe. We show that the typical time scale for the equipartition of energy among Fourier modes grows linearly with system size: this is the time scale associated with the smallest frequency present in the system. We obtain two different scaling behaviors, either with energy or with energy density, depending on the scaling of the initial condition with system size. These different scaling behaviors can be understood by a simple argument, based on the Chirikov overlap criterion. Some aspects of the universality of this result are investigated: symmetric potentials show a similar transition, regulated by the same time scale.     

A three-component Camassa-Holm system with cubic nonlinearity and peakons

In this paper, we propose a three-component Camassa-Holm (3CH) system with cubic nonlinearity and peaked solitons (peakons). The 3CH model is proven to be integrable in the sense of Lax pair, Hamiltonian structure, and conservation laws. We show that this system admits peakons and multi-peakon solutions. Additionally, reductions of the 3CH system are investigated so that a new integrable perturbed CH equation with cubic nonlinearity is generated to possess peakon solutions.     

Dynamics of entanglement in two-qubit open system interacting with a squeezed thermal bath via dissipative interaction

We study the dynamics of entanglement in a two-qubit system interacting with a squeezed thermal bath via a dissipative system-reservoir interaction with the system and reservoir assumed to be in a separable initial state. The resulting entanglement is studied by making use of concurrence as well as a recently introduced measure of mixed state entanglement via a probability density function which gives a statistical and geometrical characterization of entanglement by exploring the entanglement content in the various subspaces spanning the two-qubit Hilbert space. We also make an application of the two-qubit dissipative dynamics to a simplified model of quantum repeaters.     

Quantum-classical correspondence and mechanical analysis of a classical-quantum chaotic system

Quantum-classical correspondence is affirmed via performing Wigner function and a classical-quantum chaotic system containing random variables.The classical-quantum system is transformed into a Kolmogorov model for force and energy analysis.Combining different forces,the system is divided into two categories:conservative and non-conservative,revealing the mechanical characteristic of the classical-quantum system.The Casimir power,an analysis tool,is employed to find the key factors governing the orbital trajectory and the energy cycle of the system.Detailed analyses using the Casimir power and an energy transformation uncover the causes of the different dynamic behaviors,especially chaos.For the corresponding classical Hamiltonian system when Planck's constant h→0,the supremum bound of the system is derived analytically.Difference between the classical-quantum system and the classical Hamiltonian system is displayed through trajectories and energies.Quantum-classical correspondences are further demonstrated by comparing phase portrait,kinetic,potential and Casimir energies of the two systems.     

螺旋光纤系统中非绝热条件几何相移

由于绝热条件几何相位量子逻辑门存在非绝热差错与退相干差错这一冲突，因此在拓扑量子计算中需要设计非绝热条件几何相门，以克服这一不足.证明螺旋光纤系统内光子有效哈密顿量恰好是一个Wang Matsumoto型哈密顿量，因此螺旋光纤系统能自动产生非绝热条件几何相移.同时还证明在螺旋光纤方案中，由极化光子与螺旋光纤相互作用哈密顿量所导致的动力学相位为零（这正是拓扑量子计算所要求的），以及在螺旋光纤系统中可以通过控制极化光子初始波矢，从而较容易获得条件初始态.总之，螺旋光纤系统方案能自动满足Wang与Matsumoto的核磁共振方案中为实现非绝热条件几何相移所提出的全部条件与要求. 关键词： 几何相位 螺旋光纤系统 Wang Matsumoto型哈密顿量 拓扑量子计算     

Instantaneous frequencies of a chaotic system

The structure and geometry of high-dimensional, complex dynamical systems is usually hidden under a profusion of numerical data. We show that time-frequency analysis allows one to analyze these data regardless of the number of degrees of freedom. Our method takes snapshots of the system in terms of its instantaneous frequencies defined as ridges of the time-frequency landscape. Using the wavelet transform of a single trajectory, it can characterize key dynamical properties like the extent of chaos, resonance transitions and trappings. Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affilié à la FRUMAM (FR 2291).     

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.