Complex dynamics in a prey predator system with multiple delays

The complex dynamics is explored in a prey predator system with multiple delays. Holling type-II functional response is assumed for prey dynamics. The predator dynamics is governed by modified Leslie-Gower scheme. The existence of periodic solutions via Hopf-bifurcation with respect to both delays are established. An algorithm is developed for drawing two-parametric bifurcation diagram with respect to two delays. The domain of stability with respect to τ₁ and τ₂ is thus obtained. The complex dynamical behavior of the system outside the domain of stability is evident from the exhaustive numerical simulation. Direction and stability of periodic solutions are also determined using normal form theory and center manifold argument.     

一种新的局部时间积分的区域分解波形松弛算法

提出一种新的区域分解波形松弛算法, 使得可以在不同的子域采用不同的时间步长来并行求解线性抛物方程的初边值问题. 与传统的区域分解波形松弛算法相比, 该算法可以通过预条件子来加快收敛速度, 并且对内存的需求大大降低. 给出了局部时间步长一种具体的实现方法, 证明了离散解的存在唯一性, 并在时间连续水平分析了预条件系统. 数值实验显示了新算法的有效性.     

On linear extremal problems in the class of schlicht functions

The form of the Schiffer differential equation puts severe restrictions on the class of functions that can occur as extremal functions for arbitrary coefficient-functionals of finite degree. Theorem 1 characterizes the algebraic extremal functions for coefficient-functionals of finite degree. Furthermore it is shown that the extremal function either is an algebraic function or it must possess a non-isolated singularity, or must have a transcendental branch-point. The results are closely related to the Malmquist-Yosida theorems. However Nevanlinna's Theory of Value Distribution is not the mainly used tool but the special form of the Schiffer differential equation and the multiplicity of certain values together with the Great Picard Theorem are exploited.     

A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which sire-plifies the time-delay system the relation is discussed for into a delay-free one. Firstly, two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.     

块三对角线性方程组的一类二维区域分解并行不完全分解预条件

基于二维重叠区域分解,对每个子区域上局部不完全LU分解所得到的上、下三角因子分别进行组合,给出一类全局并行不完全分解型预条件.所给出的并行化方法适用于任何不完全LU分解型预条件.对采用二维区域分解与一维区域分解时所得并行预条件的并行计算性能进行分析比较.实验结果表明,提出的并行化方法普遍优于加性Schwarz并行化方法,且当处理器个数相对较多时采用二维区域分解优于一维区域分解.     

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper,a new analytical method of symplectic system.Hamiltonian system,is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain.In the system,the fundamental problem is reduced to all eigenvalue and eigensolution problem.The solution and boundary conditions call be expanded by eigensolutions using ad.ioint relationships of the symplectic ortho-normalization between the eigensolutions.A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space.The results show that fundamental flows can be described by zero eigenvalue eigensolutions,and local effects by nonzero eigenvalue eigensolutions.Numerical examples give various flows in a rectangular domain and show effectivenees of the method for solving a variety of problems.Meanwhile.the method can be used in solving other problems.     

Stability domains of the vertical equilibrium state of a triple simple pendulum

The stability boundaries for the vertical equilibrium position of a triple simple pendulum subject to asymmetric follower force are analyzed. The effect of the upper spring and the magnitude of the follower force on the roots of the characteristic equation is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 122–134, October 2008.     

AgGaGeS_4晶体介电性能的初步探讨

利用本实验室生长的红外非线性晶体材料AgGaGeS_4(AGGS),常温下进行腐蚀实验并观察畴结构,测试了不同频率、电压下晶体的电滞回线以及同一电压下不同频率介质的电容值.腐蚀图像显示出畴结构,畴尺寸5～10 μm左右,证实AGGS为一热释电晶体.然而,室温下的电滞回线变形为一近似椭圆,介质电容与电场频率关系表现出强色散特性.本文对这一现象进行了系统分析,最后提出了进一步探索AGGS铁电性质的具体建议.     

Understanding a time reversal process in Lamb wave propagation

This study investigates the time reversal process (TRP) of Lamb wave signals which are transmitted and received by piezoelectric transducers bonded on plate-like structures. A number of previous studies have paid attention to spatial and temporal refocusing capability of an original excitation through the TRP in highly dispersive and complex media. However, when the TRP is applied to Lamb waves in a homogeneous regular waveguide, the refocusing capability is limited due to permanent residual side bands even if the duration of the time reversed signal increases. Based on the reciprocity of elastodynamics and linear piezoelectricity, theoretical interpretation is conducted for the main and residual side bands of the reconstructed signal in the time domain. In particular, the interpretation includes the temporal effect of velocity and amplitude dispersions, the existence of multimodes, and the reflections from boundaries during the TRP. Then, numerical and experimental tests are conducted to validate the theoretical findings of this paper. Practical issues for the successful implementation of the TRP of Lamb waves are briefly addressed as well.     

Synchronization in delayed map lattices with scale-free interactions

In this paper, we study synchronization of delayed map lattices with scale-free interactions. By numerical simulations and theoretical analysis, we find that time delays influence the network synchronization but the heterogeneity seems to have little effect on network synchronization, yet no synchronization happens with the homogeneously topological structures.