一类带毒生化反应竞争模型中的极限环

研究两个微生物竞争同一营养,而其中一个竞争者会产生毒素抑制另一竞争者且产物系数为γ1(S)=A1+B1Sn和γ2(S)=A2+B2Sm(n和m是自然数)函数时的生化反应模型.分析了平衡点的稳定性,并证明了三维系统经历Hopf分支后产生的周期解的稳定性,进一步又证明极限环存在于有关的二维稳定流形之上,并用实例验证了结果.     

考研竞赛试题中的积分上限函数相关问题

介绍考研及竞赛试题中的积分上限函数相关问题,指出求解此类问题的关键.     

进位吸引子与拓扑熵

Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system.     

非线性Schroedinger方程的整体吸引子

本文讨论了一类带调和势｜x｜^2的非线性Schroedinger方程解的长时间行为，证明了整体吸引子的存在性．     

The Attractor of Fibonacci-like Renormalization Operator

In this paper we extend the Fibonacci-like maps to a wider class with the so-called "bounded combinatorics". The Fibonacci-like renormalization operator R is defined and we show that the orbit of each map from this class converges to a universal limit under iterates of R.     

KGS格点系统的全局吸引子

考虑了对应于Klein-Gordon-Schrdinger方程的格点系统(KGS格点系统)的解的长时间行为．首先通过引入一个加权范数与采用解的“切尾”法,证明了全局吸引子的存在性．在此基础上,采用元素分解法与多面体的球覆盖性质, 得到了此吸引子的Kolmogorov δ-熵的上界的一个估计．最后,我们用有限维的常微分方程的全局吸引子逼近它．     

非线性抛物型方程组的最大吸引子

利用能量积分、Sobolev空间的嵌入定理和不变区域,本文证明了一类具有"自然结构条件"的非线性抛物型方程组的最大吸引子的存在性,并给出了一定条件下解的衰减性估计。     

Lower Semicontinuity of a Non-Hyperbolic Attractor

The unstable invariant set near a non-hyperbolic stationarypoint of an abstract parabolic equation is studied. Lower semicontinuityof the attractor for the Chafee-Infante problem in the caseof the non-hyperbolic zero stationary solution is proved.     

黏弹性和热黏弹性方程的全局吸引子

该文证明了一类黏弹性和热黏弹性方程在没有外部阻尼情况下的全局吸引子的存在性.     

Hasegawa-Mima方程的整体吸引子

考虑了带有耗散项的Hasegawa-Mima方程解的长时间性态, 研究了具有初值周期边值条件的Hasegawa-Mima方程的整体吸引子问题．运用关于时间的一致先验估计,证明了该问题整体吸引子的存在性,并获得了整体吸引子的维数估计．     

耗散MKdV方程的指数吸引子

讨论了无界区域R~1上的MKdV方程,运用带权空间构造一类紧算子和算子分解的方法,得到该方程在H~2（R~1）上指数吸引子的存在性.     

Exponential Attractor for a Nonlinear Boussinesq Equation

This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.     

Global Attractor of Hindmarsh-Rose Equations in Neurodynamics

Global dynamics for a new mathematical model in neurodynamics of the diffusive Hindmarsh-Rose equations on a bounded domain is investigated in this paper. The existence of a global attractor and its regularity are proved through uniform estimates showing the dissipative properties and the asymptotically compact and smoothing characteristics.     

具阻尼的KdV—KSV方程的整体吸引子

本文证明了有阻尼的、没有Ｍａｒａｎｇｏｎｉ效应的ＫｄＶ－ＫＳＶ方程的周期初值问题存在整体吸引子,并且给出了该吸引子的Ｈａｕｓｄｏｒｆ维数和分形维数的上界估计     

Attractor for the viscous two-component Camassa-Holm equation

This paper is concerned with the attractor for a viscous two-component generalization of the Camassa-Holm equation subject to an external force, where the viscosity term is given by a second order differential operator. The global existence of solution to the viscous two-component Camassa-Holm equation with the periodic boundary condition is studied. We obtain the compact and bounded absorbing set and the existence of the global attractor in H²×H² for the viscous two-component Camassa-Holm equation by uniform prior estimate and many inequalities.     

具有进位吸引子的区间映射

对于一个具有n-进位吸引子的区间连续映射,证明了：“n不是2的方幂”是该映射具有正拓扑熵的充分条件但不是必要条件；探讨了函数方程f~3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子．     

弱D-拉回指数吸引子的存在性

主要研究弱D-拉回指数吸引子的存在性.首先讨论了弱D-拉回指数吸引子与非紧性测度之间的关系,其次,建立了弱D-拉回指数吸引子存在性的一般方法,最后证明了外力项具有指数增长速度的反应扩散方程在H_0~1(Ω)中存在弱D-拉回指数吸引子.