Existence of Periodic Solutions of an Autonomous Damped Wave Equation in Thin Domains

For a nonlinear autonomous damped wave equation in a thin domain we provide conditions ensuring the existence of periodic solutions in time. Our approach uses both methods developed by Hale and Raugel and methods based on the topological degree theory together with some results on the functionalization of parameter.     

非自治系统用瞬态响应求周期解稳定度的方法

根据Floquet理论关于线性周期系数系统解的性质及稳定性条件,定义了衡量非线性非自治系统周期解受扰后的衰减速率指标-稳定度.从动力系统流的概念出发,给出了利用非线性非自治系统稳态周期解受扰后的瞬态响应信息计算周期解稳定度的方法.以不平衡滑动轴承-弹性转子系统为例,说明了该方法的有效性.将稳定度等于零作为临界判据,该方法不仅解决了工频周期解失稳边界的确定问题,而且解决了渐进稳定域的估计和抗冲击扰动裕度的计算问题.     

Periodic Trajectories near Degenerate Equilibria in the Hénon-Heiles and Yang-Mills Hamiltonian Systems

This paper deals with connected branches of nonstationary periodic trajectories of Hamilton equations

Stable Periodic Motion of a System Using Echo for Position Control

We study a system of equations which is based on Newton's law and models automatic position control by echo. Rewritten as a delay differential equation with state-dependent delay the model defines a semiflow on a submanifold in the space of continuously differentiable maps [-h, 0] ². All time-t maps and the restriction of the semiflow given by t > h are continuously differentiable. For simple nonlinearities and suitable parameters we find a set of initial data to which the solution curves return, after an excursion into the ambient manifold. The associated return map is semiconjugate to an interval map. Estimates of derivatives yield a unique, attracting fixed point of the latter, which can be lifted to the return map. The proof that the resulting periodic orbit is stable and exponentially attracting with asymptotic phase involves a Poincaré return map and a discussion of derivatives of its iterates.     

受外激励二阶参变系统的周期解及其稳定性

给出受外激励二阶参变系统周期解的新的计算方法，它对于相当广泛一类方程均可适用，并可对解的稳定性作出判断。     

STABILITY ANALYSIS OF LINEAR AND NONLINEAR PERIODIC CONVECTION IN THERMOHALINE DOUBLE－DIFFUSIVE SYSTEMS

ＳＴＡＢＩＬＩＴＹＡＮＡＬＹＳＩＳＯＦＬＩＮＥＡＲＡＮＤＮＯＮＬＩＮＥＡＲＰＥＲＩＯＤＩＣＣＯＮＶＥＣＴＩＯＮＩＮＴＨＥＲＭＯＨＡＬＩＮＥＤＯＵＢＬＥ－ＤＩＦＦＵＳＩＶＥＳＹＳＴＥＭＳＺｈａｎｇＤｉｍｉｎｇ（张涤明）;ＬｉＬｉｎ（李琳）;ＨｕａｎｇＨ...     

求解非线性振动问题的一种新方法

首先把描述非线性振动的微分方程归结为一非线性积分微分方程，然后把此积分微分方程的求解转化为一无穷阶的非线性代数方程组的求解。从理论上讲，可得到满足任何精度要求的周期解。本文用此方法对Ｄｕｆｉｎｇ系统进行了分析。     

一类非自治动力系统超次谐周期解的不存在性

在非线性动力系统的研究中,Melnikov函数被广泛地用来作为微扰哈密顿系统是否发生次谐或超次谐分岔乃至混沌的判据. 但是在大多数情况下,经典的Melnikov方法往往只给出存在次谐周期解的结论. 产生该结果的原因被归之为在经典的Melnikov方法中只采取了一阶近似,因而高阶Melnikov方法被发展用来判断超次谐周期解的存在性. 本文对一类非自治微分动力系统进行了研究,证明了在这样一类系统中如果存在周期解则只可能是次谐周期解,超次谐周期解不可能存在,并进一步证明了在一类平面问题中所定义的旋转(R)型超次谐周期解同样不可能存在.作为该结论的一个应用,文中考察了几个典型的算例,结果表明现有的二阶Melnikov方法判断平面扰动系统是否存在超次谐周期解的结论是不恰当的,并提供了一个简单的几何上的解释.     

强非线性系统的频闪法

本文给出了求强非线性系统周期解的频闪法,并给出了该方法的数学证明。