粒子在 Hénon-Heiles势中的逃逸动力学模拟

利用庞加莱截面和相空间轨迹方法对粒子在Hénon-Heiles势中的逃逸动力学进行了模拟.粒子的动力学性质敏感地依赖于粒子的能量.数值计算表明当能量很小时,粒子的运动是规则的;随着能量的增加,粒子的运动开始出现混沌.当能量增加到鞍点能Es时,几乎所有的相空间轨迹都是混沌的.当粒子的能量E>Es,粒子可以越过势阱发生逃逸.对于给定的大于Es的能量, 我们画出了粒子的逃逸-时间曲线和逃逸轨迹.我们的研究对于研究混沌传输和逃逸动力学具有一定的参考价值.     

A new perturbation solution for systems with strong quadratic and cubic nonlinearities

The new perturbation algorithm combining the method of multiple scales (MS) and Lindstedt–Poincare techniques is applied to an equation with quadratic and cubic nonlinearities. Approximate analytical solutions are found using the classical MS method and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. For the case of strong nonlinearities, solutions of the new method are in good agreement with the numerical results, whereas the amplitude and frequency estimations of classical MS yield high errors. For strongly nonlinear systems, exact periods match well with the new technique while there are large discrepancies between the exact and classical MS periods. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniform K-theory,and Poincaré duality for uniform K-homology

We revisit ?pakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology.We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with uniform K-homology and prove Poincaré duality between uniform K-theory and uniform K-homology on spin^c manifolds of bounded geometry.     

A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations

Due to uncertain push-pull action across boundaries between different attractive domains by random excitations,attractors of a dynamical system will drift in the phase space,which readily leads to colliding and mixing with each other,so it is very difficult to identify irregular signals evolving from arbitrary initial states.Here,periodic attractors from the simple cell mapping method are further iterated by a specific Poincare’ map in order to observe more elaborate structures and drifts as well as possible dynamical bifurcations.The panorama of a chaotic attractor can also be displayed to a great extent by this newly developed procedure.From the positions and the variations of attractors in the phase space,the action mechanism of bounded noise excitation is studied in detail.Several numerical examples are employed to illustrate the present procedure.It is seen that the dynamical identification and the bifurcation analysis can be effectively performed by this procedure.     

Global positive periodic solutions of age-dependent competing systems

This paper is to investigate positive periodic solutions of a biological system composed of two competing species. The existence and uniqueness of nonnegative solutions to the model for a set of given vital rates and initial distribution are treated and the contractive property of the solutions explored. Based on these results, some simple conditions for the global existence of positive periodic orbits are established by means of Horn’s asymptotic fixed point theorem.     

球面Sn+p(c)中子流形的拓扑

研究了球面Sn+p(c)子流形Mn的Pinching定理,证明了当s＜2√n-1c时,Mn(n＞3)与n维球面同胚.     

关于二阶常微分方程周期解的定理

本文研究非自治非线性二阶常微分方程存在周期解的充分条件．在满足本文定理的条件下，作者证明所研究的二阶方程在相空间中的Ｐｏｉｎｃａｒｅ映射是平面上有奇点的动力系统，从而证明原方程有周期解．这一结果全面推广已有的若干结论．     

On the Chaotic Instability of a Nonsliding Liquid-Filled Top with a Small Spheroidal Base via Melnikov-Holmes-Marsden Integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.     

Dynamical analysis of two coupled parametrically excited van der Pol oscillators

The dynamical behavior of two coupled parametrically excited van der pol oscillators is investigated in this paper. Based on the averaged equations, the transition boundaries are sought to divide the parameter space into a set of regions, which correspond to different types of solutions. Two types of periodic solutions may bifurcate from the initial equilibrium. The periodic solutions may lose their stabilities via a generalized static bifurcation, which leads to stable quasi-periodic solutions, or via a generalized Hopf bifurcation, which leads to stable 3D tori. The instabilities of both the quasi-periodic solutions and the 3D tori may directly lead to chaos with the variation of the parameters. Two symmetric chaotic attractors are observed and for certain values of the parameters, the two attractors may interact with each other to form another enlarged chaotic attractor.     

THE GENERAL PROPERTIES OF THE SPHERICAL VORTICES（SV）OF n－TH ORDER AND THE CHAOTIC PHENOMENA AND OF THE ORDERED STRUCTURES OF THE SV OF 3RD ORDER

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