共查询到18条相似文献,搜索用时 67 毫秒
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运用Liapunov第二方法讨论了一类四阶非线性系统的全局渐近稳定性,通过构造出较好的Liapunov函数,获得到了其零解全局渐近稳定的充分性准则,去掉了一般要求Liapunov函数具有无穷大这个较强的条件,并推广了部分文献所研究的非线性系统. 相似文献
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It is well known,that in the theory of stability in differential equations,Liapunov's second method may be the most important The center problem of Liapunov's second method is construction of Liapunov function for concrete problems.Beyond any doubt,construction of Liapunov functions is an art.In the case of functional differential equations,there were also many attempts to establish various kinds of Liapunov type theorems.Recently Burton[2]presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However,the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton,we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability.Those criteria improve the result of literature[1]and they are with simple forms,easily checked and applicable. 相似文献
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本文利用Liapunov泛函与Liapunov函数方法建立了无穷时滞脉冲泛函微分方程基于两种测度的一致稳定和一致渐近稳定的一个新的定理,并通过实例说明了所获结论的应用. 相似文献
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基于奇异谱分析的降噪方法及其在计算最大Liapunov指数中的应用 总被引:1,自引:0,他引:1
基于奇异谱分析对信号的自适应滤波特性,提出了一种降低混沌信号噪声的算法,这个算法首先求得信号的各阶经验正交函数(EOF)和主分量(PC),然后用经验正交函数和主分量重构信号,根据重构信号的奇异谱选择最优的重构阶次以获得降噪后的信号.在计算动力系统最大Liapunov指数时,由于噪声的存在会降低计算的精度,因此将提出的降噪算法应用于最大Liapunov指数的计算中.通过对Henon映射和Logistic映射这两个典型混沌系统最大Liapunov指数的计算,结果表明该算法能有效提高最大Liapunov指数计算的精度. 相似文献
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A DELAY DIFFERENTIAL INEQUALITY 总被引:3,自引:0,他引:3
In this paper, we obtain a slight generalization of the celebrated Halanay delay differential inequality[1]. Using this inequality, Liapunov function and vector Liapunov function, we show that our result can be applied to the stability behavior of solutions of some delay differential systems. And also, we attempt to relax some restrictions of dv/dt, which is necessary under Liapunov function's method on the delay differential systems. 相似文献
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一类不连续系统关于闭不变集的有限时间稳定性研究 总被引:1,自引:0,他引:1
主要研究右端不连续系统在Filippov解意义下关于闭不变集(未必是紧集)的有限时间稳定问题.当Liapunov函数是Lipschitz连续的正则函数情况下,给出了相关的Liapunov稳定性定理. 相似文献
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讨论了一类脉冲泛函微分方程的渐近稳定性.通过改进 Liapunov泛函的上界,利用Liapunov泛函第二方法和Jensen不等式,得到了一个一致稳定性定理和一个一致渐近稳定性定理,给出的例子说明了所得结果的优越性. 相似文献
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S. L. Ziglin 《Regular and Chaotic Dynamics》2010,15(4-5):630-633
We prove the absence of an additional meromorphic first integral in the Riemann problem on the motion of a homogeneous liquid ellipsoid with zero angular and vortex momenta in the case of zero self-gravitation. 相似文献
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V. G. Zadorozhniy 《Computational Mathematics and Mathematical Physics》2013,53(4):486-502
For three-dimensional vortex motion, a linear mathematical model with random coefficients is considered, and formulas for the first two moment functions of solutions are derived. The conditions are found under which a linear chaotic resonance occurs; i.e., the mean angular velocity of the motion increases. The results show that the energy of the vortex increases because of the chaotic motions present in the flow. 相似文献
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研究了航天器编队飞行多目标姿态跟踪鲁棒控制问题.主航天器装有一个快速机动天线和一个星载相机.考虑相机对地面目标跟踪,同时考虑天线与从航天器通信的空间任务.通过引入角速度约束和姿态角约束,分别推导了相机和天线的参考姿态角、角速度和角加速度.提出期望逆系统的概念,将三维空间姿态跟踪问题转化为调节问题,简化了控制器的设计.考虑存在参数摄动和外部干扰力矩的情况,基于期望逆系统和滑模控制,设计了鲁棒姿态跟踪控制器,并利用Liapunov稳定性理论证明了控制系统的渐近稳定性.以两航天器编队飞行多目标跟踪为例进行数值仿真,结果表明所设计的控制器具有良好的鲁棒性和优越的跟踪性能. 相似文献
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We consider a planar particle system obeying a generalized Pauli exclusion principle. In the mean field approximation, this system is described by a Schrödinger equation we recently introduced, containing a complex nonlinearity. The particle number, the total energy, and the angular momentum are conserved in such a system. We consider vortexlike stationary solutions of the form
and write the differential equation for the vortex shape. We find an analytic solution of this equation and obtain a closed expression for the vortex profile. We investigate some mean properties and, in particular, calculate the energy spectrum and angular momentum of the vortex. 相似文献
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It is well known, that in the theory of stability in differential equations, Liapunov's second method may be the most important. The center problem of Liapunov's second method is construction of Liapunov function for concrete problems. Beyond any doubt, construction of Liapunov functions is an art. In the case of functional differential equations, there were also many attempts to establish various kinds of Liapunov type theorems. Recently Burton [2] presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However, the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton, we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability. Those criteria improve the result of literature [1] and they are with simple forms, easily checked and applicable.This project is supported by the National Natural Science Foundation of China. 相似文献
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We investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda, and Damodaran and Zakharov . We first establish rigorously the existence of a pair of almost parallel vortex filaments, with opposite circulation, colliding at some point in finite time. The collision mechanism is based on one of the self‐similar solutions of the model, described by the authors in an earlier work. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with polygonal symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity.© 2016 Wiley Periodicals, Inc. 相似文献
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The vortex lattice method is improved for modeling nonlinear highly nonstationary processes appearing in an interaction of bodies that undergo an irregular motion in a proximity of solid boundaries with large-scale vortex structures. We show that keeping the condition of freezing the vortex buildups in the medium leads, in the vortex lattice method, to eliminating the arbitrariness in the calculated time step, singularity radius, and the buffer-zone radius.For the ensemble of discrete vortices that model the surface of tangential discontinuity of the velocity, we propose an economical method for solving the Cauchy problem. The method decreases the discretization error related to the replacement of this surface with a system of discrete vortices.A test for the improved vortex lattice method has been conducted for a nonstationary nonlinear problem on nonharmonic angular oscillations of a wing in a stationary medium near a solid surface in the case where there is no gap between the wing and the surface.By using the improved vortex lattice method, one succeeded, for the first time, in obtaining a solution of a problem of this type that converges from the numerical point of view. A comparison of the obtained results with known experimental data shows a good agreement. 相似文献
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This paper presents a numerical study of the vortex eccentricity in a gas cyclone and its effect on the performance of the cyclone. The gas flow in the cyclone was modeled as an unsteady flow by the Navier–Stokes equations with the Reynolds Stress Model (RSM) as the turbulence model. The particles were modelled by the Lagrangian particle tracking (LPT) approach in an unsteady gas flow. Gas cyclones with the same dimensions and total flow rates but different numbers of inlets were simulated with the inlet velocity varying from 12 to 20 m/s. The vortex eccentricities in different cases were analyzed in terms of radial deviation and angular deviation. In addition, the frequency of the precessing vortex core (PVC) was analyzed by the fast Fourier transform (FFT). The results show that the vortex center in the single inlet cyclone has a great eccentricity and its precession center is also different from the geometric center, which reduces the particle collection efficiency. The increase in the symmetry of the inlet causes only a very small increase in the pressure drop in the simulated cases, but it can significantly reduce the vortex eccentricity, particularly by eliminating the eccentricity of the PVC center. The improvement of the vortex eccentricity can generally increase the collection efficiency for particles greater than 2.0 µm. The increase of the collection efficiency is mainly because the symmetrical vortex can restrain the short-circuiting flow of particles. The results can improve the understanding of the vortex flow in gas cyclones which may guide the optimization of gas cyclones. 相似文献