共查询到19条相似文献,搜索用时 203 毫秒
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非光滑动力系统胞映射计算方法 总被引:4,自引:0,他引:4
针对非光滑动力学系统特点,在胞映射思想基础上,引入拉回积分等分析手段,得到了非光滑系统吸引子和吸引域的胞映射计算方法.并以一类碰振系统为例,给出了其吸引子和具有复杂分形边界的吸引域,并验证了该方法的有效性. 相似文献
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本文用点映射--胞地对强迫Van Der Pol振子的周期吸引子和吸引域进行了数值分析、模拟了吸引子的内部结构,周期吸引子的吸引域可以达到预期的精度。 相似文献
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应用广义胞映射图论(Generalized Cell Mapping Digraph)方法,数值地研究Thompson的逃逸方程在最佳逃逸点附近的分岔。发现了嵌入在Wada分形吸引域边界上的混沌鞍,混沌鞍是状态空间不稳定(非吸引)的混沌不变集合。Wada分形吸引域边界是具有Wada性质的边界,即吸引域边界上的任意点也同时是至少两个其它吸引域的边界点,称为Wada域边界。我们证明Wada域边界上的混沌鞍导致局部鞍结分岔具有全局不确定性结局,研究了Wada域边界上混沌鞍的形成与演化,证明最终的逃逸分岔是混沌吸引子碰撞混沌鞍的边界激变。 相似文献
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Duffing-van der Pol系统的随机分岔 总被引:1,自引:0,他引:1
应用广义胞映射图论方法(GCMD)研究了在谐和激励与随机噪声共同作用下的Duffing-van
der Pol系统的随机分岔现象. 系统参数选择在多个吸引子与混沌鞍共存的范围内.
研究发现, 随着随机激励强度的增大,该系统存在两种分岔现象:
一种为随机吸引子与吸引域边界上的鞍碰撞, 此时随机吸引子突然消失;
另一种为随机吸引子与吸引域内部的鞍碰撞, 此时随机吸引子突然增大. 研究证实,
当随机激励强度达到某一临界值时,
该系统还会发生D-分岔(基于Lyapunov指数符号的改变而定义),
此类分岔点不同于上述基于系统拓扑性质改变所得的分岔点. 相似文献
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系泊海洋平台周期运动倍周期分岔的胞映射分析 总被引:1,自引:0,他引:1
应用胞映射方法研究了系泊海洋生产平台的周期运动及其倍周期分岔。系泊运动的数学模型是一个具有指数回复力特性的非线性强迫振子 ,以波浪作用力为外激励。将波浪激励周期作为分岔控制参数 ,研究了周期系泊运动的倍周期分岔。胞映射方法用于寻找系统的稳定吸引子并确定其吸引域。时间历程、相图、功率谱和Poincar啨映射用于确定吸引子的具体类型芯糠⑾?,分岔参数处于不同的区域时 ,系统存在着相异的倍周期分岔特性。观察到了倍周期分岔的产生和突然消失 ,也找到了一个趋于吸引子的倍周期分岔序列。根据吸引域的胞映射分析结果解释了上述不同的倍周期分岔特征。发现其原因在于倍周期序列中的每个吸引子是否具有全局吸引性。 相似文献
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非线性强迫Mathieu方程的激变和瞬态混沌 总被引:1,自引:0,他引:1
应用广义胞映射图论(GCMD)方法研究了非线性强迫Mathieu方程的激变、瞬态混 沌、以及随系统参数变化的全局分岔特性.揭示了参数激励常微分系统混沌吸引子的边界激变 是由于混沌吸引子与其吸引域边界上的不稳定周期轨道发生碰撞而产生的,发现了边界激变产 生的瞬态混沌,在Poincaré截面上直观地表明了瞬态混沌的几何空间结构,以及瞬态混沌的空 间结构随着系统参数逐渐远离激变临界值的衰变.给出了对自循环胞集进行局部细化的方法. 相似文献
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This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed points is defined, which makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective than the cell 相似文献
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全局分析的广义胞映射图论方法 总被引:8,自引:2,他引:6
应用广义胞映射理论的离散连续状态空间为胞状态空间的基本概念,依循Hsu的将偏序集和图论理论引入广义胞映射的思想,以集论和图论理论为基础,提出了进行非线性动力系统全局分析的广义胞映射图论方法.在胞状态空间上,定义二元关系,建立了广义胞映射动力系统与图的对应关系,给出了自循环胞集和永久自循环胞集存在判别定理的证明,这样可借助国论的理论和算法来确定动力系统的全局性质.应用图的压缩方法,对所有的自循环胞集压缩后,在全局瞬态分析计算中瞬态胞的总数目得到有效地减少,并能借助于图的算法有效地实现全局瞬态的拓扑排序.在整个定性性质的分析计算中,仅采用布尔运算. 相似文献
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This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems
into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number
of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping
given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process
for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative
technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the
deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed points is defined, which
makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective
than the cell mapping methodl[1]. And an example for two-dimensional mapping is given. 相似文献
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分析了图胞映射方法在处理非光滑动力系统过程中遇到的关键问题------胞流扩张. 为了有效减小胞流扩张, 基于迭代图胞映射方法, 通过引入人工顶点集的概念, 构建了非光滑系统迭代图胞映射具体实施方案, 讨论了在此过程中值得注意的事项. 结合典型实例分析, 证实了该方法的有效性. 相似文献
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When solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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The method of cell-to-cell mapping has the potential to be a very effective and general method of global analysis for strongly non-linear systems. However, simple cell mappings being integer mappings, most of the classical methods of analysis based upon continuity and differentiability of the mapping are no longer applicable and, therefore, new notions need be introduced. In [6] the concept of singular multiplets is introduced for the cell functions associated with the cell mappings. In this paper we study the characteristics of these singular entities by examining the mapping properties of the cells in the singular entities and in their neighborhoods. The key tool used in classifying the mapping properties is the limit set of the mapping process of a cell. The work represents a continuing effort to develop the method of cell-to-cell mapping as a tool of global analysis and to provide the method with a sound and appropriate structure. 相似文献
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A new type of cell mapping, referred to as an adjoining cell mapping, is developed in this paper for autonomous dynamical systems employing the cellular state space. It is based on an adaptive time integration employed to compute an associated cell mapping for the system. This technique overcomes the problem of determining an appropriate duration of integration time for the simple cell mapping method. Employing the adjoining mapping principle, the first type of algorithm developed here is an adaptive mapping unraveling algorithm to determine equilibria and limit cycles of the dynamical system in a way similar to that of the simple cell mapping. In addition, it is capable of providing useful information regarding the behavior of dynamical systems possessing pathological dynamics and of systems with rapidly changing vector field. The adjoining property inherent in the adjoining cell mapping method, in general, permits development of new recursive algorithms for unraveling dynamics. The required computer memory for a practical implementation of such algorithms is considerably less than that required by the simple cell mapping algorithm since they allow for a recursive partitioning of state space for trajectory analysis. The second type of algorithm developed in this paper is a recursive unraveling algorithm based on adaptive integration and recursive partitioning of state space into blocks of cells with a view toward its practical implementation. It can find equilibria of the system in the same manner as the simple cell mapping method but is more efficient in locating periodic solutions. 相似文献
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齿轮副中的齿距偏差等短周期误差使系统出现复杂的周期运动, 影响齿轮传动的平稳性. 将该类复杂周期运动定义为近周期运动, 采用多时间尺度Poincaré映射截面对其进行辨识. 为研究齿轮副的近周期运动, 引入含齿距偏差的直齿轮副非线性动力学模型, 并计入齿侧间隙与时变重合度等参数. 采用变步长4阶Runge-Kutta法数值求解动力学方程, 由所提出的辨识方法分析不同参数影响下系统的近周期运动. 根据改进胞映射法计算系统的吸引域, 结合多初值分岔图、吸引域图与分岔树状图等研究了系统随扭矩与啮合频率变化的多稳态近周期运动. 研究结果表明, 齿轮副中的短周期误差导致系统的周期运动变复杂, 在微观时间尺度内, 系统的Poincaré映射点数呈现为点簇形式, 系统的点簇数与实际运动周期数为宏观时间尺度的Poincaré映射点数. 短周期误差导致系统在微观时间尺度内的吸引子数量增多, 使系统运动转迁过程变复杂. 合理的参数范围及初值范围可提高齿轮传动的平稳性. 该辨识与分析方法可为非线性系统中的近周期运动研究奠定理论基础. 相似文献
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This paper investigates the experimental dynamics of a beam structure that supports an attached rigid body and that can impact
a comparatively compliant base structure. The problem area is motivated by impact phenomena that are observed in certain structures
internal to nuclear reactors. The assembly is subjected to base excitation at specified frequency and acceleration, and the
resulting displacement and velocity time histories are recorded and used to obtain spectra, phase diagrams, and Poincaré sections.
The measurements validate simulation results obtained by using a constraint and modal mapping method based on the two sets
of modes when the structure is in-contact, and when it is not-in-contact. Generalized coordinates are mapped across the impact
discontinuities in the modal representation. The forced response simulation predicts the test specimen’s response over a range
of excitation frequencies. The specimens are fabricated as single integral structures from acrylnitrile butadene styrene plastic
through rapid prototyping technology in order to eliminate the undesirable dissipation and flexibility arising from joints
and connections. The experimental system can exhibit complex response characteristics, and the influences on complexity of
deadband clearance and of asymmetry in the point of impact are examined in the experiments. 相似文献