MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting.We obtain an accurate homogenization result.We also show that as the nonlinear term depends on the microscopic time variable,the global homogenized problem thus obtained is a system consisting of two hyperbolic equations.It is also shown that in spite of the presence of several time scales,the global homogenized problem is not a reiterated one.     

Quadratic Lyapunov Function and Exponential Dichotomy on Time Scales

In this paper, we study the relationship between exponential dichotomy and quadratic Lyapunov function for the linear equation x△=A（t）x on time scales. Moreover, for the nonlinear perturbed equation x△= A（t）x ＋ f（t, x） we give the instability of the zero solution when f is sufficiently small.     

EXISTENCE OF PERIODIC SOLUTIONS TO A SYSTEM WITH FUNCTIONAL RESPONSE ON TIME SCALES

This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.     

含噪音高频数据动态整合估计波动率的方法

时间域和状态域方法是两种常见的非参数估计方法.前者主要使用的是最近的历史数据,而后者则主要依赖于过去的历史信息.本文在时间域上,通过对含噪音高频数据采用双时间尺度方法获得其波动率,进而获得经动态整合后的波动率.     

带有变时滞延迟和分布延迟的竞争型神经网络周期解在时间尺度上的的全局指数稳定性

In this paper, competitive neural networks with time-varying and distributed delays are investigated. By utilizing Lyapunov functional methods, the global exponential stability of periodic solutions of the neural networks is discussed on time scales. In addition, an example is given to illustrate the effectiveness of the theoretical results.     

吸收型双光子光学双稳态的时间行为

利用多重时间尺度微扰分析方法,研究了一个半经典吸收型双光子光学双稳系统的时间演化行为。一级近似结果表明,在高透射分支附近,系统的长时间行为由输出场振幅的方程所支配,其它动力学量除绝热地跟随场振幅变化而外,还有快速振荡。而在低透射分支附近,所有动力学变量都通过长时间尺度变化,没有与短时间尺度相联系的振荡行为。稳定态在高透射分支与低透射分支之间的跃变可以由简单的方程描述。 关键词：     

On the horizontal distribution of algal-bloom in Chaohu Lake and its formation process

Based on the remote sensing images of algae, the present work analyzes the horizontal distribution characteristics of algal blooms in Chaohu Lake, China, which also reveals the frequency of algal blooms under different wind directions. Further, an unstructured-grid, three-dimensional finite-volume coastal ocean model （FVCOM） is applied to investigate the wind-induced currents and the transport pro- cess to explain the reason why algal blooms occur at the detected places. We first deduce the primary distribution of biomass from overlaid satellite images, and explain the formation mechanism by analyzing the pollution sources, and simulating the flow field and transportation process under prevailing wind over Chaohu Lake. And then, we consider the adjustment action of the wind on the corresponding day and develop a two-time scale approach to describe the whole formation process of algae horizontal distribution in Chaohu Lake. That is, on the longer time scale, i.e., during bloom season, prevailing wind determines the primary distribution of biomass by inducing the characteristic flow field; on the shorter time scale, i.e., on the day when bloom occurs, the wind force adjusts the primary distribution of biomass to form the final distribution of algal bloom.     

计及短周期误差的直齿轮副近周期运动及其辨识

齿轮副中的齿距偏差等短周期误差使系统出现复杂的周期运动, 影响齿轮传动的平稳性. 将该类复杂周期运动定义为近周期运动, 采用多时间尺度Poincaré映射截面对其进行辨识. 为研究齿轮副的近周期运动, 引入含齿距偏差的直齿轮副非线性动力学模型, 并计入齿侧间隙与时变重合度等参数. 采用变步长4阶Runge-Kutta法数值求解动力学方程, 由所提出的辨识方法分析不同参数影响下系统的近周期运动. 根据改进胞映射法计算系统的吸引域, 结合多初值分岔图、吸引域图与分岔树状图等研究了系统随扭矩与啮合频率变化的多稳态近周期运动. 研究结果表明, 齿轮副中的短周期误差导致系统的周期运动变复杂, 在微观时间尺度内, 系统的Poincaré映射点数呈现为点簇形式, 系统的点簇数与实际运动周期数为宏观时间尺度的Poincaré映射点数. 短周期误差导致系统在微观时间尺度内的吸引子数量增多, 使系统运动转迁过程变复杂. 合理的参数范围及初值范围可提高齿轮传动的平稳性. 该辨识与分析方法可为非线性系统中的近周期运动研究奠定理论基础.      

THREE POSITIVE SOLUTIONS TO BVP FOR p-LAPLACIAN IMPULSIVE FUNCTIONAL DYNAMIC EQUATIONS ON A TIME SCALE

In this paper, we axe interested in the existence of three positive solutions to a BVP for p-Laplacian impulsive functional dynamic equations on a time scale. Using the five-functional fixed theory, we establish a Banach space and an appropriate operator. In this paper, we combine the delta-nabla p-Laplacian BVP with impulsive functional dynamic equations, and obtain some new sufficient conditions for the existence of three positive solutions to the BVP, and our result here generalizes the previous related results.     

Boundedness of solutions of second order nonlinear dynamic equations

This paper deals with the boundedness of the solutions of the following dynamic equations(r(t)x△(t))△+a(t)f(xσ(t))+b(t)g(xσ(t))=0and(r(t)x△(t))△+a(t)xσ(t)+b(t)f(x(t-τ(t)))=e(t)on a time scale T.By using the Bellman integral inequality,we establish some suffcient conditions for boundedness of solutions of the above equations.Our results not only unify the boundedness results for differential and difference equations but are also new for the q-difference equations.