ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

IntroductionThepreciseintegrationmethod(PIM) [1],whichwasproposedforsolvingstructuraldynamicequations.Thismethodissimplerandpossesseshigherprecision .Forlinearsteadystructuraldynamicsystems,itsnumericalresultsattheintegrationpointsarealmostequaltothatoftheexactsolutioninmachineaccuracy .InthepreciseintegrationmethodforsolvingPDEs,theequationsshouldbediscretizedinthephysicalspaceforobtainingthesystemofODEsintime ,whichisoftenexecutedbythefinitedifferencemethodorthefiniteelementmethod .Inrec…     

一类反应扩散方程中的螺旋波

本文主要利用摄动方法，将λ－ω系统的结论推广到一般的反应扩散方程中，得到一般反应扩散方程的螺旋波解的存在定理。本定理可应用于一类反应扩散方程。     

结构力学的动态不稳定性

在本回顾性文章中,作者着重论述在结构的稳定性和超临界行为中需要采用动力学方法进行分析的问题．它们包括以下的动态不稳定性：（１）参数激励振动;（２）在冲击载荷下的结构响应;（３）空气－弹性和流体－弹性诱发的动态不稳定性;（４）在所谓随动力作用下的结构响应;（５）输气或输液管道的不稳定性;（６）转子由于转动摩擦或有关因素引起的不稳定性;（７）旋涡诱发的不稳定性;（８）构件的断裂作为一类动态不稳定性．本文的重点放在早期发展历史、开拓性的研究和基本概念,尤其是那些在过去产生过争论但至今在某些方面仍有启发性的题材．与此同时,还讨论一些新近结果和未来研究展望．     

抽运参数随时间慢变所诱发Laser-Lorenz方程的分岔与光学双稳态

提出了新的简便的方法研究具有入射信号的半经典Laser-Lorenz方程-由于抽运参数随时间慢变,导致分岔滞后,并诱发暂态的光学双稳态-通过量级平衡和用线性化系统的慢变解作近似,给出了分岔转迁的量级关系和暂态光学双稳态发生的条件,并通过数值计算给出分岔转迁区间和暂态光学双稳态的滞后环- 关键词：     

Strongly resonant bifurcations of nonlinearly coupled van der Pol-Duffing Oscillator

IntroductionThecomplicateddynamicalbehaviorofnonlinearoscillatorsystemsisafrontiertopicinthestudyofnonlineardynamicsatthepresent,whichplaysanimportantroleinrealityandareconnectedcloselywithmanydynamicalproblemsinengineering.Generallyspeaking,therearenogeneralmethodstofindouttheprecisesolutionsofnonlineardifferentialequahonswhichdescribenonlinearoscillatorsystems.Since1920s,scholarshavebeensearchingforcommonlyaPPlicableasymptoticalmethods,andtherehavebeensomespeCialbooks,suchas[1~4]etc..Howev…     

van der Pol型时滞系统的两参数余维一Hopf分岔及其稳定性

研究具有三次非线性时滞项的ｖａｎ ｄｅｒ Ｐｏｌ型时滞系统随两参数（时滞量和增益系数）余维一Ｈｏｐｆ分岔,说明了线性化特性方程随两参数变化时的根的分布和Ｈｏｐｆ分岔存在性;通过构造中心流形并且使用范式方法确定出Ｈｏｐｆ分岔的方向以及周期解的稳定性;分析了时滞量对所论系统发生Ｈｏｐｆ分岔的影响。     

Non-Gaussian Colored Noise Optimized Spatial Coherence of a Hodgkin-Huxley Neuronal Network

We numerically study how non-Gaussian colored noise affects the spatial coherence of a Hodgkin-Huxley neuronal network. From the simulation results, we find that there exists some intermediate noise intensities, correlation time of the colored noise, and the deviation from Gaussian colored noise, for which an ordered pattern with a characteristic spatial frequency of the system comes forth in a resonant manner. Namely, under certain conditions, spatial coherence of the studied neuronal network can be optimized by the non-Gaussian colored noise, which indicates the occurrence of spatial coherence resonance.     

Complete Synchronization in Coupled Chaotic HR Neurons with Symmetric Coupling Schemes

Chaos synchronization in an array of coupled chaotic neurons with symmetric coupling is investigated. A criterion for the stability of the synchronization manifold is deduced by transforming the variational equation of the coupled system into a block diagonal one, and the critical coupling strengths for synchronization in different coupled cases are given. As examples for illustration, the HR neurons with the open-ended （i.e. chain）, ring, star and all-to-all （i.e. global） coupling schemes are considered. It is shown that the coupling scheme plays an important role in synchronization and information transmission of neurons.     

具阶段结构害虫防治模型的脉冲效应

对于用微分方程描述的种群生态动力系统，其研究结果已十分丰富，但自然界中的许多变化规律都呈现出脉冲效应，因此用脉冲微分方程描述某些运动状态在固定或不固定时刻的快速变化或跳跃更切合实际，尤其在刻画种群生长和流行病动力学行为方面，脉冲微分方程的描述显得更科学更真实，具有脉冲效应的种群动力学模型的研究目前还处于刚刚起步阶段，本对符合实际的有脉冲效应的具阶段结构的常系数害早防治模型进行了研究，得到了系统存在周期解的充分条件，系统存在唯一周期解的充分条件，系统周期解轨道渐近稳定的充分条件。     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.