A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

On reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance

This paper addresses the reachable set bounding for discrete-time switched nonlinear positive systems with mixed time-varying delays and disturbance, which contains switched linear positive systems as a special case. By resorting to a new method that does not involve the common Lyapunov–Krasovskii functional one, explicit criteria to ensure any state trajectory of the system converges exponentially into a prescribed sphere are obtained under average dwell time switching. The results can then be extended to more general time-varying systems. Finally, two numerical examples are used to demonstrate the effectiveness of the obtained results.     

双色中红外激光场延迟及相位调控产生水窗区间光子

理论研究了双色中红外激光场时间延迟及相位对高次谐波光谱的影响.结果表明：当激光延迟为-1.0 fs,激光相位为0.2π和0时,谐波截止能量可以得到有效延伸,并且获得一个超宽水窗区间谐波连续平台区.此外,谐波光谱的延伸与控制场波长关系不大,即,在上述激光延迟和相位下,控制场波长在2300 nm到2700 nm区间时都可获得水窗区谐波光谱.最后,叠加光谱连续区的谐波可获得35 as的水窗区孤立阿秒脉冲.     

Dynamics of milling processes with variable time delays

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration

This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes. Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through experimentation.     

Delay Model for a Cycling Transport Through Porous Medium

A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed.     

主动隔振中气动压力跟踪的预测控制研究

气动伺服系统的压力跟踪是主动隔振系统中的一个重要环节。本文根据气动伺服系统的特点，建立了系统压力工作点的模型，应用基于状态空间的预测控制方法对系统压力进行了轨迹跟踪控制。首先，提出了一种控制器切换的方法来消除压力跟踪过程中的稳态误差；其次，通过对预测控制算法的改进减小了滞后对闭环系统动态性能和稳定性的影响。实验表明，本文提出的方法有效地解决了主动隔振系统中的气动压力跟踪问题。     

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｂｉｌｉｔｙｏｆｔｈｅｉｎｔｅｒｖａｌｍａｔｒｉｘａｎｄｕｎｃｅｒｔａｉｎｓｙｓｔｅｍｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｒｅｓｅａｒｃｈｅｒｓｉｎｔｈｅｐａｐｅｒｓ [1 -1 3 ] .Ｔｈｅｓｔａｂｉｌｉｔｙａｎｄαｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｔｈｅｆｏｌｌｏｗｉｎｇｉｎｔｅｒｖａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｗｉｔｈｓｉｎｇｌｅｔｉｍｅｄｅｌａｙ ｘ(ｔ) =Ｎ[Ｐ ,Ｑ]ｘ(ｔ) +Ｎ[Ｃ ,Ｄ]ｘ(ｔ-τ)ｈａｖｅｂｅｅｎｃｏｎｓｉ…     

Noise and stability in differential delay equations

We study the stability of linear stochastic differential delay equations in the presence of additive or multiplicative white and colored noise. Using a stochastic analog of the second Liapunov method, sufficient conditions for mean square and stochastic stability are derived.