Fold-Hopf bifurcation in a simplified four-neuron BAM (bidirectional associative memory) neural network with two delays

The bidirectional associative memory (BAM) neural network with four neurons and two delays is considered in the present paper.A linear stability analysis for the trivial equilibrium is firstly employed to provide a possible critical point at which a zero and a pair of pure imaginary eigenvalues occur in the corresponding characteristic equation.A fold-Hopf bifurcation is proved to happen at this critical point by the nonlinear analysis.The coupling strength and the delay are considered as bifurcation parame...     

PUBLICATIONS ON THERMAL STRESSES

The study of the nonlinear response of sandwich flat panels exposed to thermomechanical loading systems is the topic of this article. The sandwich structure considered in this article consists of a thick core layer bonded by the face layers, which are assumed to be symmetrically located with respect to the midplane of the overall structure. The loads involved in this analysis consist of biaxial compressive edge loads, a lateral pressure, and a nonuniform temperature field. The effects of the unavoidable initial geometric imperfections and the character of tangential boundary conditions are incorporated, and their implications upon the structural response are explored. In short, the results of this study are intended to provide pertinent information on the thermomechanical load-carrying capacity of flat sandwich structures.     

Stability and Neimark–Sacker bifurcation in Runge–Kutta methods for a predator–prey system

We investigate the discretization of a predator–prey system with two delays under the general Runge–Kutta methods. It is shown that if the exact solution undergoes a Hopf bifurcation at τ=τ*, then the numerical solution undergoes a Neimark–Sacker bifurcation at τ(h)=τ*+O(h ^p ) for sufficiently small step size h, where p≥1 is the order of the Runge–Kutta method applied. The direction of Neimark–Sacker bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.     

Complicated motion of particles on vibration screen surface

lINTRODUCTIONToday,them0tiontheoryofparticlesonscreensurfaceisanimp0rtantresearchdirectionofscreeningtechn0logyandtheory['~8].Bymeansofstudyingmotionregularityofparticles,wecanobtaintheoptimumkineticparametersfortheindustrialscreeningandraiseitsefficien-cy.Thematerialbeingscreenedhasvariableshapeandsize,withdifferentsurfacemoistureandclaymineralscontents.Themotionofparti-clesisaffectedbydisplacement,velocity,accel-erationofscreensurfaceandfrictionamongpar-ticles.S0theparticles'motiononscr…     

A boundary equation of the principal period-2 component in the degree-n bifurcation set

The degree-n bifurcation set is a generalized Mandelbrot set for the complex polynomial P _c (z)=z ⁿ +c. The boundary of the principal period-2 component in the degree-n bifurcation set is first defined and then formulated by a parametrization of its image, which is the unit circle under the multiplier map. We investigate the boundary equation using the geometric symmetry of the degree-n bifurcation set with respect to rays of symmetry in the complex plane. In addition, an algorithm drawing the boundary curve with Mathematica codes is proposed.     

断裂顶板锚拉支架支护系统的分叉行为

应用弹性系统稳定性理论对断裂顶板－锚拉支架系统建立了动力系统稳定性分析的力学模型．对该模型分别考虑因块ＡＢ（或ＢＣ）沿对角线变形和支座处的水平变形引起的稳定性进行了求解；讨论了解曲线即平衡路径的稳定性及系统的静态分叉特征；进而分析了断裂顶板结构的运动失稳机制，并给出了该系统的运动稳定条件，证实了借助当代非线性科学研究岩土工程问题的必要性和理论意义．     

Probability Response of Shape Memory Alloy Beam Subjected to Noise Excitation

噪声激励下形状记忆合金梁的概率响应

李玉婷,冯进钤,王迎宵

（西安工程大学 理学院,西安 710000）

摘要：

形状记忆合金是一种具有记忆效应和超弹性的材料,广泛应用于各个工程领域中。 基于弹性理论和Galerkin方法,本文提出了具有刚性约束的形状记忆合金梁的振动模型。应用随机平均法,得到该模型的概率响应。同时,通过数值模拟验证解析结果的正确性,从而证明了该随机平均法的有效性。 此外,讨论了随机分岔现象。 结果表明,一定的碰撞恢复力和阻尼力会引起P分岔。

关键词：形状记忆合金;随机平均;稳态概率密度;随机分岔

     

基于动态轧制力的波纹辊轧机非线性振动

 金属层状复合板波纹辊轧制成形技术是一项变革性技术。为研究动态轧制力对波纹辊轧机振动特性和分岔行为的影响,考虑了波纹辊轧机动态轧制力、波纹界面间的非线性刚度和非线性阻尼,建立了基于动态轧制力的波纹辊轧机非线性振动数学模型。运用多尺度法求解了波纹辊轧机辊系在动态轧制力激励下的非线性振动幅频特性方程。分析了动态轧制力幅值、非线性刚度系数和非线性阻尼系数等参数对非线性振动的影响。通过最大Lyapunov指数、分岔混沌图、Poincaré截面和相轨迹等方法分析了轧制力的动态变化对系统稳定性的影响,设计了分岔反馈控制器对轧制力动态变化诱发的分岔行为进行控制,并且通过数值仿真验证了控制器设计的正确性和可行性。     

河流分汊成因与演变机制研究综述

基于较系统的文献调研,介绍了分汊形成机制如中心沙坝沉积、横向沙坝转换、斜槽切断、复合沙坝切割和河道决口,水沙分配影响因素如汊道几何形态、汊道河床地形、汊道内的水力特性和潮汐等因素,和水沙分配计算方法等主要方面的研究进展,并以长江中下游分汊河段为例,总结了其分汊河道的水力特征和演变规律。最后探讨了分汊河道研究中还需解决的问题,以及数值模拟方法在分汊形成与演变研究中的应用及前景。     

Chaos in parametric resonance flow at water-mercury interface

In the electrochemical system with liquid-liquid interface, intense local convections by the resonance with potential pulses take place. Therefore, with laser beam scattering, temporal movement of the water-mercury interface was observed. As a result, the scattering efficiency showed non-linear oscillation.

Such non-linear response could be controlled by potential pulse height. As the potential height was increased, new scattering peaks in the oscillation emerged, which was expected of a kind of bifurcation phenomenon. From these results, phase portrait, Poincarè section, correlation dimension of the strange attractor and the largest Lyapunov exponent of the trajectories were obtained. Consequently, it was concluded that all the parameters indicate chaotic behavior of the resonance flow.