高阶非线性时滞方程振动的充要条件及比较定理

本文首先给出了高阶非线性时滞微分方程所有解振动的充要条件。然后利用该结果，得到了一些振动的比较定理，解决了张炳根猜想。     

中立型脉冲微分方程正解的存在性

利用压缩映射原理，讨论了中立型脉冲时滞微分方程正解的存在性。     

二阶非线性中立型时滞差分方程的正解存在性和振动性

研究了一类二阶非线性中立型时滞差分方程△^2（x（n）＋^m∑i=1Pi（n）x（n-ki））＋q（n）f（x（n-σ））=0的最终正解的存在性，并得出了其解振动的充分条件.     

An oscillatory neural network and dynamical associative memory

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从众心理引起博弈策略的同步振荡

在著名的博弈模型"石头-布-剪刀"模型中加入从众心理的影响,考察从众心理对系统动力学的影响. 其中对利益的渴求和从众心理两个机制相互竞争.从复杂系统科学的角度来看,从众心理在网络中的个体之间起到了很好的耦合作用.当从众心理占据上风时,这种耦合作用可以引起个体之间博弈策略的同步振荡,进而形成宏观的振荡现象.在社会学的某些领域中,这种宏观振荡往往造成不良的后果.所以,如果期望一个稳定的多样策略共存的状态,就要尽力降低从众心理对策略选择的影响.     

带强迫项的二阶脉冲时滞微分方程的振动性

研究带强迫项的二阶脉冲时滞微分方程的振动性,得到了若干判别此类方程振动的充分性条件,所得结果推广并改进了时滞微分方程的振动性理论中某些已知的相关结果.     

ENSO影响热带大气季节内振荡的年代际变化特征

为了研究厄尔尼诺和南方涛动(ENSO)现象影响热带大气季节内振荡(ISO)的年代际变化特征,利用奇异值分解(SVD)、小波分析和经验正交函数分析(EOF)等方法对热带大气ISO强度指数、赤道中东太平洋海温及热带大气环流场进行了分析。计算结果显示,20世纪70年代中期以前,ENSO对热带大气ISO的影响较弱;70年代中期以后,ENSO对热带大气ISO的影响加强。造成上述年代际变化的原因与热带大气环流的年代际变化有关,因此,ENSO对热带大气ISO的影响也存在年代际变化。     

Two-port network model and startup criteria for thermoacoustic oscillators

The startup process of a thermoacoustic engine is a self-excited oscillation process generated in inhomogeneous acoustic media. To reveal these coupling relations between various influential factors is an important task of basic research on thermoacoustics. In this paper thermoacoustic engines are regarded as thermoacoustic oscillators consisting of the active network and the passive network. Accordingly, the two-port Y-parameter for relevant component is derived, and standing wave and traveling wave thermoacoustic engine are described by the negative-resistance and feedback model, respectively. The relevant two-port network topology is given as well. The startup criteria for thermoacoustic oscillators are obtained by using Nyquist instability criterion. The model prediction of startup parameters, particularly, startup frequency and mode characteristic are in agreement with that of experimental results reported in the literature. Moreover, with topological graphs it is verified that standing wave engines would start up in a negative-resistance state and there would exist high frequency modes in thermoacoustic-Stirling engines. By investigating into the frequency response of thermoacoustic system, this method proposed can achieve such an objective that these effects of operating and structural parameters of engine on startup modes and startup temperature can be revealed in an analytical way. Thus this approach to test and check thermal stability can be provided in a design phase, instead of using empirical frequency to design thermoacoustic systems. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by National Natural Science Foundation of China (Grant Nos. 50576024 and 51076013)     

不可压缩Ogden材料组成的球壳的有限振动

研究了由一类各向同性不可压缩Ogden材料组成的球壳在突加拉伸载荷作用下的有限振动问题。首先利用平衡微分方程、边界条件和初始条件求得了球壳径向对称运动的微分方程,证明了存在一个临界值。当拉伸载荷未达到这个临界值时,随着时间的增加,球壳的内表面将做非线性周期振动;当拉伸载荷超过这个临界值时,球壳最终会破裂。最后给出了相应的数值算例。     

二阶非线性中立型微分方程的振动性

研究了一类二阶非线性中立型微分方程的振动性,建立了此类方程的所有解振动的充分条件.