Lax方程与耦合Poisson流形的动力r-矩阵

对于一个与Poisson流形耦合的动力r-矩阵,我们在相应的Lie双代数胚上构造出一类Lax方程和一族守恒量,希望利用该方法进一步研究可积Hamilton系统.     

Structure of Pareto optima in an infinite-horizon economy where agents have recursive preferences

This article generalizes the one-agent growth theory with discounting to the case of several agents with recursive preferences. In a multi-consumption goods world, we show that, under some regularity conditions, any Pareto optimum can be viewed as a function of a trajectory of a dynamical system. The state space can be chosen to be the product of the space of capitals and the unit simplex. We define and study the properties of generalized value functions.     

高维离散动力系统的平稳振荡

本文应用不动点原理研究了高维离散周期系统的存在周期解的唯一性和稳定性,给出了存在平稳振荡和唯一周期解的充分条件.     

Lattice vibrational properties of uranium pnictides

Lattice vibrational properties of uranium pnictides have been studied using breathing shell model (BSM) which includes breathing motion of electrons of the U-atoms due tof−d hybridization. The phonon dispersion curves of U-pnicitides calculated from the present model agree reasonably well with the measured data. A comparison has been made between BSM and our results reported earlier obtained from three-body force rigid ion model to reveal the importance of the short-range electron-phonon interactions in these compounds. We also report, for the first time, the two phonon density of states and specific heat for these compounds.     

一种新的混沌同步及保密通信方式

本文提出一种新的混沌同步及保密通信方式。在发送端，将信息信号与混沌载波的和经取模运算后再嵌入混沌动力系统的迭代之中以实现调制；在接收端，用一个相应的非动力学系统从接收信号中提取混沌载波并进而恢复信息信号。研究表明，该混沌同步方式具有较强的抗干扰能力并且实现容易；该保密通信系统保密性能良好。     

Integrable Deformation of Gaussian Distribution and the Ornstein-Uhlenbeck Process

An integrable deformation of one-dimensional Gaussian distribution in terms of a continuous Moser hierarchy is described explicitly. Here the hierarchy governs the level dynamics of the semi-infinite Toda molecule. The action of the second-order flow is shown to be equivalent to that of the Ornstein–Uhlenbeck diffusion process.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Finite-time stabilization of state dependent impulsive dynamical linear systems

The problem of finite-time stabilizing control design for state-dependent impulsive dynamical linear systems (SD-IDLS) is tackled in this paper. Such systems are characterized by continuous-time, linear, possibly time-varying, dynamics coupled with discrete-time, linear, possibly time-varying, dynamics. The continuous-time part determines the system evolution in any time interval between two consecutive resetting events, while the discrete-time part governs its instantaneous state jump whenever the system trajectory intersects a resetting set, i.e. a region of the state space assumed to be time-independent. By making use of a quadratic control Lyapunov function, the finite-time stabilization of SD-IDLS through a static output feedback control design is specifically discussed in this paper. A sufficient and constructive result is provided based on the conical hulls of the resetting set subregions and on some cone copositivity properties of the chosen control Lyapunov function. Such a result is based on the solution of a feasibility problem that involves a set of coupled Difference/Differential Linear Matrix Inequalities (D/DLMI), which is shown to be less conservative and more numerically amenable with respect to other results available in the literature. An example illustrates the effectiveness of the proposed approach.     

DYNAMICAL FORMATION OF CAVITY FOR COMPOSED THERMAL HYPERELASTIC SPHERES IN NONUNIFORM TEMPERATURE FIELDS

Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials were discussed under the case of a non-uniform temperature field and the surface dead loading. The mathematical model was first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load was obtained by using the variable transformation method. By numerical computation, critical loads and cavitation growth curves were obtained for different temperatures. The influence of the temperature and material parameters of the composed sphere on the void formation and growth was considered and compared with those for static analysis. The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.