多频谐和与噪声作用下Flickering振子的安全盆侵蚀与混沌

研究了催化反应Flickering振子在多频率确定性谐和外力和有界随机噪声联合作用下,系统安全盆的侵蚀和混沌现象.将Melnikov方法推广到包含有限多个频率外力和随机噪声联合作用的情形,推导出了系统的随机Melnikov过程,根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值,然后用数值模拟方法计算了系统的安全盆分岔点.结果表明,由于随机扰动的影响,系统的安全盆分岔点发生了偏移,并且使得混沌容易发生.同时证明,激励频率数目的增加扩大了参数空间上的混沌区域,也使得安全盆分岔提 关键词： 多频率激励 Flickering振子 安全盆 混沌     

New bifurcations of basin boundaries involving Wada and a smooth Wada basin boundary

This paper demonstrates and analyses double heteroclinic tangency in a three-well potential model, which can produce three new types of bifurcations of basin boundaries including from smooth to Wada basin boundaries, from fractal to Wada basin boundaries in which no changes of accessible periodic orbits happen, and from Wada to Wada basin boundaries. In a model of mechanical oscillator, it shows that a Wada basin boundary can be smooth.     

单向航道散货港口船舶调度优化

为提高单向航道散货港口的泊位利用率,研究多港池的散货港口船舶调度优化问题。考虑船舶间需保持安全航行距离、进出港时段交替条件和成簇进出港规则等现实约束,以进港船舶总等待时间最小为目标,构建了混合整数线性规划模型。基于问题的特点,设计了启发式规则与模拟退火算法相结合的混合算法进行求解。在数值实验中分别将该算法的结果同下界值和两种现实调度方案对比。结果表明,运用混合算法求解的结果与下界值的平均相对偏差为5.28%,较两种现实调度方案的目标值优化率提升显著,且平均泊位优化率分别为6.74%和4.71%,验证了方案及算法的有效性。     

Invariant curves for planar competitive and cooperative maps

In this paper we present results on the existence of invariant curves for planar maps that are monotone with respect to either the south-east or north-east ordering. Some of these curves are the stable or unstable manifolds of hyperbolic fixed points (saddle points) or non-hyperbolic fixed points, and are also the boundary of basins of attraction of such points.     

On Stability and Persistence of Some Oligopoly Models

A dynamic oligopoly model is given. Its steady state and stability and the bounds of its basin of attraction are studied. Delay (memory) is then introduced. Oligopoly is then reformulated using Smale's game which is more realistic than ordinary games since it takes memory into consideration. Persistence is studied for some oligopoly models.     

渭河盆地东南部砂土液化模糊综合评价及洪水影响研究

依据砂土液化影响因素和大量实际资料对渭河盆地东南部5县进行了砂土液化模糊综合评价, 给出了砂土液化分区, 并讨论了洪水泛滥对该区砂土液化的影响。     

Influence of Initial Conditions on the Postcritical Behavior of a Nonlinear Aeroelastic System

The behavior of a nonlinear, non-Hamiltonian system in the postcritical (flutter) domain is studied with special attention to the influence of initial conditions on the properties of attractors situated at a certain point of the control parameter space. As a prototype system, an elastic panel is considered that is subjected to a combination of supersonic gas flow and quasistatic loading in the middle surface. A two natural modes approximation, resulting in a four-dimensional phase space and several control parameters is considered in detail. For two fixed points in the control parameter space, several plane sections of the four-dimensional space of initial conditions are presented and the asymptotic behavior of the final stationary responses are identified. Amongst the latter there are stable periodic orbits, both symmetric and asymmetric with respect to the origin, as well as chaotic attractors. The mosaic structure of the attraction basins is observed. In particular, it is shown that even for neighboring initial conditions can result in distinctly different nonstationary responses asymptotically approach quite different types of attractors. A number of closely neighboring periodic attractors are observed, separated by Hopf bifurcations. Periodic attractors also are observed under special initial conditions in the domains where chaotic behavior is usually expected.     

Numerical Simulation for Evolutionary History of Three-Dimensional Basin

ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＦＯＲＥＶＯＬＵＴＩＯＮＡＲＹＨＩＳＴＯＲＹＯＦＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＢＡＳＩＮＹｕａｎＹｉ－ｒａｎｇ（袁益让）；ＷａｎｇＷｅｎ－ｑｉａ（王文洽）；ＹａｎｇＤａｎ－ｐｉｎｇ（羊丹平）（Ｄｅｐａｒｔｍｅ...     

Natural harmonic oscillations of a heavy fluid in basins of complex shape

The natural harmonic oscillations of a heavy fluid in uniform-depth basins of complex shape, including those with three or more symmetry axes, are investigated within the shallow-water approximation. The waves are assumed to be gently sloping. The modes found are compared with the similar modes in an elliptic basin representing the class of basins with two symmetry axes. The mode characteristics associated with the number of basin symmetry axes and the basin shape are explored. Basins with two symmetry axes whose shape differs considerably from the elliptic, in particular, nonconvex basins, are considered. Both rotating and non-rotating basins are studied. The possibility of approximating the amplitudes of certain rotating-basin mode classes by Bessel functions is discussed.     

多稳态串联折纸结构的非线性动力学特性

折纸结构和折纸力学超材料由于其无穷的设计空间、出色的变形能力、超常规力学特性和广泛的应用前景,最近受到了学术界和工程界的 广泛关注.特别地,某些折纸结构单胞由于具有独特的双稳态特性而获得深入研究.注意到折纸结构和折纸超材料通常由多胞构成,但多胞 结构的多稳态特性及其诱发的动力学行为尚不清晰,相关的研究还较少.本文在双稳态Miura-ori堆叠结构单胞的基础上,研究由两个异构 双稳态单胞基于力平衡串联而成的结构.静力学分析指出,双胞串联结构具有4个定性不同的稳定构型,呈现出多稳态特征.动力学分析指 出,双胞串联结构在4个稳定构型处具有显著不同的固有频率特征. 逐渐增大激励幅值,双胞串联结构的多稳态特性诱发出类型丰富的复杂 非线性动力学响应,包括亚谐、超谐甚至混沌的阱内和阱间振动. 根据幅值特征,我们将稳态动力学响应分为九类,并开展了动力学响应的 吸引盆和吸引盆稳定性分析.结果表明,不同类型动力学响应的吸引盆稳定性(即出现概率)显著不同,且与激励幅值密切相关.本文得到的 多稳态双胞串联结构的静力学特性、动力学响应的分类,以及吸引盆稳定性相对于激励幅值的演化规律,对深入认识多稳态折纸结构的非 线性动力学特性,调控非线性动力学响应具有参考价值和指导意义.