1:2 and 1:3 internal resonance active absorber for non-linear vibrating system

Vibration and dynamic chaos should be controlled in either structures or machines. An active vibration absorber for suppressing the vibration of the non-linear plant when subjected to external and parametric excitations is studied in the presence of one-to-two and one-to-three internal resonance. The main attention is focused on the study of the active control and stability of two systems, which can be used to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to determine four first-order non-linear ordinary differential equations that govern the modulation of the amplitudes and phases in the presence of internal resonance of the two systems with quadratic and cubic order of control. These equations are used to determine the steady state solutions and their stability. The stability study of non-linear periodic solution for two cases (1:2 and 1:3 internal resonance) and the stability of the obtained numerical solution are investigated using frequency, force-response curves and phase-plane method. Also, effects of some parameters on the steady state solution of the vibrating system are investigated and reported in this paper. Variation of some parameters leads to the bending of the frequency, force-response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work.     

The stability problem and special solutions for the 5-components Maxwell–Bloch equations

For the 5-components Maxwell–Bloch system the stability problem for the isolated equilibria is completely solved. Using the geometry of the symplectic leaves, a detailed construction of the homoclinic orbits is given. Studying the problem of invariant sets for the system, we discover a rich family of periodic solutions in explicit form.     

非自治时滞微分系统的周期解

本文将一类非自治时滞微分方程变换为等价的哈密顿系统.这样求解此时滞微分系统可以等价于求解相应的哈密顿系统.运用Floquet变换和辛变换方法,建立了此类微分系统多重周期解的存在性定理,此结果推广了先前文献中的一些结果.     

长贮产品基于贮存可靠度的序贯检测方法

长贮产品在贮存过程中,性能会逐步退化直至失效,保持和恢复系统可靠性的一种极为有效的方法就是周期地测试贮存产品的关键性能,并且修复和更换所发现的故障产品.检测时间间隔过长,则产品贮存可靠性达不到要求;检测时间过短,不仅要耗费大量的人力、物力甚至会诱发失效.考虑到产品贮存状态变化的复杂性,论文提出了Weibull分布产品基于贮存可靠度的序贯检测方法,可以动态调整检测间隔期,并结合仿真实例给出了序贯模型和参数估计方法.     

Characterization of local sampling sequences for spline subspaces

The sampling theorem is one of the most powerful tools in signal analysis. It says that to recover a function in certain function spaces, it suffices to know the values of the function on a sequence of points. Most of known results, e.g., regular and irregular sampling theorems for band-limited functions, concern global sampling. That is, to recover a function at a point or on an interval, we have to know all the samples which are usually infinitely many. On the other hand, local sampling, which invokes only finite samples to reconstruct a function on a bounded interval, is practically useful since we need only to consider a function on a bounded interval in many cases and computers can process only finite samples. In this paper, we give a characterization of local sampling sequences for spline subspaces, which is equivalent to the celebrated Schönberg-Whitney Theorem and is easy to verify. As applications, we give several local sampling theorems on spline subspaces, which generalize and improve some known results.     

Periodic behavior for a degenerate fast diffusion equation

This work deals with the study of periodic solutions to a degenerate fast diffusion equation. The existence of the periodic solution to an intermediate problem restraint to a period T is proved first and then the result is extended by the data periodicity to all time real space. The approach involves an appropriate approximating problem whose periodic solution is proved via a fixed point theorem. Next, a passing to the limit procedure leads to the existence of the solution to the original problem on a time period. Finally, the behavior at large time of the solution to a Cauchy problem with periodic data is characterized.     

Global existence and nonexistence of solutions for second-order nonlinear differential equations

This paper deals with the global existence and nonexistence of solutions of the second-order nonlinear differential equation (φ(x^′))^′+λφ(x)=0${(\phi (x^{\prime }))}^{\prime }+\lambda \phi (x)=0$ satisfying x(0)=_x0$x(0)=x_0$ and x^′(0)=_x1$x^{\prime }(0)=x_1$, where λ   is a positive parameter and φ:(−ρ,ρ)→(−σ,σ)$\phi :(-\rho ,\rho )\to (-\sigma ,\sigma )$ with 0<ρ?∞$0<\rho ?\infty$ and 0<σ?∞$0<\sigma ?\infty$ is strictly increasing odd bijective and continuous on (−ρ,ρ)$(-\rho ,\rho )$. Necessary and sufficient conditions are obtained for the initial value problem to have a unique global solution which is oscillatory and periodic. Examples are given to illustrate our main result. Finally, a nonexistence result for the equation with a damping term is discussed as an application to our result.     

Nearly Comonotone Approximation of Periodic Functions

Suppose that a continuous 27r-periodic function f on the real axis changes its monotonicity at points y_1:-π≤ y_(2s)y_(2s-1)… y_1 π,s ∈ IN.In this PaPer,for each n≥N,a trigonometric polynomial P_n of order cn is found such that:P_n has the same monotonicity as f,everywhere except,perhaps,the small intervals(y_i-π/n,y_i+π/n)and‖f-P_n‖c(s)ω_3(f,π/n),where N is a constant depending only on mini=1,...,2s {y_i-y_(i+1)},c,c(s) are constants depending only on s,ω_3(f_1,·) is the modulus of smoothness of the 3-rd order of the function f,and ||·|| is the max-norm.     

Dynamics in a diffusive predator–prey system with strong Allee effect and Ivlev-type functional response

The dynamics of a kind of reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. We prove the existence and uniqueness of the solution and give a priori bound. Hopf bifurcation and steady state bifurcation are studied. Results show that the Allee effect has significant impact on the dynamics.     

泛函微分方程周期边值问题的正解

讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件.