广义KdV-Burgers方程长时间性态的谱方法

1．引言随着无限维动力系统研究的发展和深入,人们对非线性发展方程长时间性态的研究越来越重视[1－6］,而这种研究在很大程度上依赖于数值计算的结果,因此,计算结果是否可靠,计算格式先得是否合适都是值得探讨和深入研究的问题17－10．广义KdV－Burg6rs方程是一类重要的非线性发展方程,在实际问题中也有着广泛的应用,因此,对它的研究即有理论价值也有实际意义．本文讨论如下的广义KdV－Burgers方程的周期初值问题其中a,q是已知实常数,且a＞0八。）,g（。）,h00是已知实函数．文［10］对上述问题构造了半离散的Fourier谱逼近…     

Ginzburg-Landau方程动力性态的Fourier谱逼近

0　引言和符号立方Schrodinger方程或更一般的形式Ginzburg-Landau方程出现在许多物理和化学问题中.例如在非线性光学的细束流中有方程2ikux+2⊥u+n2n0k2|u|2u=0对于二维流,有方程n2n0k2|u|2u=-2kiut-uxx-uyy还有等离子体的Langmuir波;一维单色波的自调制;二维定态平面波的自聚集;在非相对论下超导电子对在电磁场中运动等均可用非线性Schrodinger方程和Ginzburg-Landau方程来描述[1-4].另外,反应扩散方程描述的化学反应方程的研究中也出现Ginzburg-Landau方程,如相对于稳态浓度c*的扰动浓度c-c*就满足Ginzburg-Landau方程[5,6].由…     

Spatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte system

Spatiotemporal multiple coherence resonances for calcium activities induced by weak Gaussian white noise in coupled hepatocytes are studied. It is shown that bi-resonances in hepatocytes are induced by the interplay and competition between noise and coupling of cells, in other words, the cell in network can be excited either by noise or by its neighbour via gap junction which can transfer calcium ions between cells. Furthermore, the intercellular annular calcium waves induced by noise are observed, in which the wave length decreases with noise intensity augmenting but increases monotonically with coupling strength increasing. And for a fixed noise level, there is an optimal coupling strength that makes the coherence resonance reach maximum.     

NONLINEAR PSEUDOPARABOLIC EQUATIONS IN ARBITRARY DIMENSIONS

1.IntroductionAsiswellknownthenonlinearpseudoparabolicequationsweresuggestedandstudiedinconnectionwithmanypracticalproblemsatthebeginningofthe1970s.AmongthemtheBBMequationat box~abet~0(1'1)isthemostimportant,itwassuggestedinconnectionwiththepropagationoflongwavesinnonlineardispersivesystemsbyT.B.Benjaminetallljin1972.In1977,L.A.Medeirosetall2]studiedtheweaksolutionoftheinitialboundaryvalueproblemforageneralizedformof(1.1)RevisedJanuary,25,1995.*ThisworkissupportedbytheNationalScienceFOun…     

阈下激励与噪声联合作用下肝细胞系统的内钙时空随机共振问题

研究阈下周期信号激励对耦合肝细胞系统内钙离子浓度（［Ca²⁺］)的时空随机共振性质的影响.当阈下激励的频率等于确定性系统在Hopf分岔点附近的频率时,它就会极大地提高随机耦合系统内发生［Ca²⁺］喷发的细胞的比例,通过对喷发比的自相关函数计算得知阈下激励增强了系统在高斯白噪声作用下［Ca²⁺］的时间共振性.通过数值模拟得知,对于不同耦合强度,都存在最优噪声强度使得随机系统内［Ca²⁺］时间共振达到最佳,并且随着细胞间耦 关键词： 钙振动 噪声 阈下激励 随机共振