时滞类Lorenz系统的Hopf分支

对类Lorenz系统的状态变量加上时滞得到一个泛函微分动力系统--时滞类Lorenz系统。首先给出了该系统仅存在零平衡点的条件,然后根据系统在零平衡点处的线性化系统对应的特征方程根的分布情况,给出了系统在零平衡点处稳定性和发生Hopf分支的条件,最后通过一些数值模拟验证了所得结论的正确性。     

Numerical computations of the flow in a finite diverging channel

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff （2006） was numerically investigated. The effects of the Reynolds number, initial condition, intersection angle, length of the wedge edges, and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow, then a vortical （circulation） flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow, the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°, a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow, although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability, the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment, providing a possible explanation for the hysteresis phenomenon in the experiment.     

一类Mathieu方程的混沌控制

利用数值分析的方法,采用龙格库塔算法对Mathieu方程系统的动力学行为进行了仿真,采用周期激振力控制方法实现了系统混沌运动的控制,使系统脱离混沌运动域进入周期轨道。并根据全局分岔图对系统控制进行了分析,得出了合理的结论。     

蛋白质分子能量与信息传输方程的局域普适开折与Hopf分支

考虑了蛋白质分子能量与信息传输方程的局域普适开折，在此基础上研究了方程的Hopf分支，普适开折的Hopf分支是通有的，这有利于生命体内蛋白质分子能量与信息传输的合理解释．     

Bifurcation analysis of a microcantilever in AFM system

The atomic force microscope system (AFM) has become a popular and useful instrument to measure the intermolecular forces with atomic resolution that can be applied in electronics, biological analysis, materials, semiconductors, etc. This paper studies the bifurcation phenomenon and complex nonlinear dynamic behavior of the probe tip between the sample and microcantilever of an atomic force microscope using the differential transformation method. The dynamic behavior of the probe tip is characterized with reference to bifurcation diagrams, phase portraits, power spectra, Poincaré maps, and maximum Lyapunov exponent plots produced using the time-series data obtained from differential transformation method. The results indicate that the probe tip behavior is significantly dependent on the magnitude of the vibrational amplitude. Specifically, the probe tip motion changes from T-periodic to 3T-periodic, then from 6T-periodic to multi-periodic, and finally to chaotic motion with windows of periodic motion as the vibrational amplitude is increased from 0 to 5.0. Furthermore, it is demonstrated that the differential transformation method is in good agreement for the considered system.     

Gray-Scott模型的动态分歧分析

该文以Gray-Scott模型为研究对象,用数学的方法研究该系统的动态分歧.主要是运用线性全连续场普理论,中心流形约化方法及跃迁理论,得到了模型在一定条件下的跃迁类型的判别数,并判断了跃迁类型,给出了分歧解的表达式.     

非线性Fredholm积分方程与分岔

本文研究了非线性Frcdholm积分方程的解数随参数k变化而发生分岔的规律:Ⅰ)当k〈0时,方程至少有一个负解;当0〈k〈k_1时,方程至少有一个正解。Ⅱ)当k〉k_n时,方程至少有(2n—1)个正解。并将这些结果应用到非线性Sturm—Iiouville问题。     

幽默语言的修辞规律

幽默语言是人与人交往过程中最重要的润滑剂.语言幽默的创造,源于语言符号超常规的组合方式与认识主体的特殊心理活动过程的结合,包括岔断律、倒置律、转移律、干涉律、降格律、升格律等.掌握了幽默语言的修辞规律,就能自觉灵活地创造出幽默语言,提升与人交流的能力.     

参量激励vanderPol-Duffing系统的共振与非共振分叉

利用KBM法研究参量激励的vanderPol-Duffing非线性振动系统在除亚谐共振外的一切共振和非共振情况下的分叉问题 .利用KBM法导出了振子的分叉响应方程 ,研究了其稳定性 ,并且绘制了相图     

Bifurcation and chaos of a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields

We studied the problem of bifurcation and chaos in a 4-side fixed rectangular thin plate in electromagnetic and mechanical fields. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and the expressions of electromagnetic forces, the vibration equations are derived for the mechanical loading in a steady transverse magnetic field. Using the Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponent diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained.