Dynamics of a Modified Predator-Prey System to Allow for a Functional Response and Time Delay

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differential-algebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.     

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed.     

Stability and robustness of time‐delay systems

Abstract

Using some properties of matrix measures and matrix's spectral radius, a new stability criterion for a linear time‐delay system is derived. This result is also extended to interval time‐delay systems.     

一种基于多步回溯算法的铣削稳定性预测方法

在加工过程中,由于薄壁件的弱刚性易发生加工颤振,从而对工件表面质量和刀具寿命等造成不良的影响,对铣削过程的稳定性进行预测是至关重要的.通过提出一种多步回溯算法来预测铣削过程的稳定性,将铣削过程离散化成时滞周期方程,在每个时间间隔上采用多步回溯的方法来近似时间周期及时滞项.通过构建状态转移矩阵,根据Floquet理论获得...     

具时滞的比率型三种群捕食系统的全局渐近稳定性

研究了一类具有时滞的比率型三种群捕食者-食饵系统,给出了系统持续生存的条件。通过构造Lyapunov泛函的方法得到了该系统正平衡态全局渐近稳定的充分条件。     

大型水平轴风力发电机桨叶稳定性研究

大型水平轴风力发电机桨叶为流-刚-柔耦合的周期时变多体系统。本文暂未考虑风载荷,分析了重力载荷和桨叶预锥角、转速等因素的变化对稳定性的影响。力学建模中,考虑了桨叶挥舞、摆振、扭转和轴向运动以及根部铰的挥舞、摆振和变矩等刚体运动。利用有限元法形成5节点18自由度的刚-柔混合梁单元模型,应用Hamilton原理建立桨叶动力学方程,求得对应的摄动方程,采用Newmark隐式积分方法求解。根据Floquet理论判断运动稳定性,计算了相关转换矩阵的特征值。结果表明预锥角对桨叶运动稳定性影响不容忽视。在通常的工况下,桨叶能够稳定地运转。     

时滞合作系统的周期正解

用非线性分析的方法讨论了非自治的二维时滞合作系统,获得了周期正解的存在性定理。     

线性时滞系统的离散滑模砰砰控制方法

将滑模控制和最优砰砰控制相结合,给出了线性时滞系统的离散滑模砰砰控制方法.考虑到实际中作动器难以适应正负极值控制力间的快速切换,给出了改进的离散滑模砰砰控制方法.考虑到在地震过程中作动器无需一直对结构施加控制,给出了改进的条件离散滑模砰砰控制方法.另外文中还通过算例给出了确定作动器最大控制力的近似方法.算例结果表明,所提出控制方法能够有效地减小结构地震作用下的峰值响应,控制效果优于经典的LQR控制方法,而且所给控制方法对结构固有参数变化具有较好的鲁棒性.     

Robust stability analysis for linear uncertain time‐delay systems with delay‐dependence

Abstract

This paper proposes a sufficient robust stability condition for uncertain time‐delay systems with delay‐dependence. The results obtained include information on the delay time and is less conservative than delay‐independent results which have been published when delays are small. Examples are given to illustrate the application of our results.     

带缓冲区的基于时间延迟的可修设备联合优化

考虑到设备停机时间较长对企业经济效益的影响,在设备间设置缓冲区;同时考虑到设备单目标维修决策模型的不足,以及故障次数表达的精确程度对决策的影响,借用了时间延迟理论,建立了可修复设备的联合决策模型。为了满足设备的生产要求,以及最优化缓冲区生产系统的费用水平,将分别以平均单位时间的总停机时间、平均单位时间的总费用作为目标函数,来进行研究。通过时间延迟理论,分析了故障形成的过程,并表达出故障次数。借用更新报酬定理,来表达两目标函数。由离散迭代算法,求解得到：最优的检查周期和额定库存分别为25 d、1 195件时,总费用率在停机时间率为0.199时最小为22 739.95元。另外,进行了敏感性分析来验证最优解,最后由求解结果来指导生产线维修管理。     

延期电雷管的发火原理及影响秒量因素的探讨

本文以LYGT30D 3050毫秒延期电雷管为例,比较详细地阐述了延期电雷管的发火原理及影响秒量精度的各种因素,为延期电雷管的设计,提供了比较可靠的依据。     

Pb3 O4对硅系延期药稳定性的影响？

对硅系延期药进行了高温热冲击、高温高湿、贮存稳定性、补充部分氧化剂、调控球磨时间等方面的试验,然后分别对延期药中的铅丹质量分数及延期时间进行检测。分析发现单独对延期药进行高温热冲击试验,不会改变延期药中铅丹的质量分数;但将延期药置于高温高湿敞开环境下,铅丹质量分数却会显著降低;随着贮存时间的延续,延期药中的铅丹质量分数会逐步降低,降低至一定程度后,会引起延期雷管瞎火;在延期药原配比中补充部分氧化剂,并没有对延期药的性能产生较大的改变;在一定的范围内延长球磨时间,会导致延期药中的铅丹质量分数明显降低,但却显著提高了延期药的延期精度。     

New asymptotic stability criteria for the linear time‐delay systems

Abstract

Several new stability criteria for the linear time‐delay system represented by some simple closed regions in the complex plane are proposed. In these criteria, the system's stability can be easily determined by examining the locations of the eigenvalues of the system matrix A ₀ or its delay matrix A_d . In other words, we do not need to solve any complicated characteristic equation of the system.     

电动力绳索系统的周期解求解及其稳定性分析

摘 要：对运行在倾斜圆轨道上的电动力绳索系统的动力学特性进行了分析研究。首先建立了系统的动力学模型,分别采用摄动法及推广后的数值算法求得系统的基本周期解,并运用所给数值算法中的稳定性判据分析了周期解的稳定性,得出该系统周期运动不稳定的结论。最后进行仿真验证,结果表明在摄动量较小时,两种求解算法得到的周期解基本相同,但当摄动量较大时,摄动法求得的周期解发生了畸变,不理想此时通常借助数值算法加以求解;仿真结果同样证实了所得周期解的不稳定特性。     

基于滞后型系统理论的半主动悬架控制系统稳定性分析

为了研究时滞对于半主动悬架系统稳定性的影响,建立含时滞的二自由度半主动悬架模型,依据滞后型系统稳定性理论运用改进的全时滞稳定代数判据推导出满足系统全时滞稳定的充要条件,得到可控阻尼的取值范围。针对不符合全时滞稳定条件的半主动悬架参数,提出运用稳定性切换点分析法求取实际所需的稳定性切换点及其稳定性区间。通过时域仿真发现在全时滞稳定情况下时滞的产生并非会导致悬架性能的恶化。在非全时滞稳定的情况下,随着时滞的增加悬架性能不断下降并在超过稳定性切换点时发生剧烈恶化。     

周期性变化内热源条件下建筑蓄热对室温延迟的影响

将室内热源（包括人体、照明、设备散热及透过窗户的日射得热）强度处理为按正弦规律变化的周期函数,研究了周期性变化内热源条件下建筑的时间常数、无量纲对流换热系数、傅里叶时间常数、室内热源引起的室内温度增值变化幅度、室外温度波动幅度对室温延迟的影响规律,并给出了预测室温延迟时间的数值解。     

具有时滞和反馈控制的非自治Schoner模型持续生存和周期解

本文研究了一类具有时滞和反馈控制的非自治Schoner模型,这是一个三维系统。通过把这个三维系统转变为二维系统,并应用重合度理论,得到了该类模型至少存在一个正周期解的充分条件;并且应用分析技巧,建立了该系统一致持续生存的充分条件。