Attractors for Second Order Lattice Dynamical Systems

We consider the existence and the approximation of the global attractor for second order damped lattice dynamical systems.     

Stability and Controllability in Non-autonomous Time-discrete Dynamical Systems

In this paper stability and attractivity in non-autonomous time-discrete dynamical systems is investigated with the aid of Lyapunov functions. The results are applied to the problem of stabilization of controlled systems by feedback controls. In the final section of the paper we give sufficient conditions for norm-bounded null-controllability of linear systems.     

Exponential Attractors for Lattice Dynamical Systems in Weighted Spaces

The aim of this paper is to investigate the existence of exponential attractors for lattice reaction-diffusion systems in weighted spaces l_s²l_{\sigma}^{2} and for partly dissipative lattice reaction-diffusion systems in weighted spaces l_m²×l_m²l_{\mu}^{2}\times l_{\mu}^{2}, respectively. In contrast to the previous work by Abdallah in J. Math. Anal. Appl. 339, 217–224 (2008) and Commun. Pure Appl. Anal. 8, 803–818 (2009), we get the existence of exponential attractors for lattice dynamical systems in the weak topology spaces.     

Approximate Forward Attractors of Non-Autonomous Dynamical Systems

In this paper the forward asymptotical behavior of non-autonomous dynamical systems and their attractors are investigated. Under general conditions, the authors show that every neighborhood of pullback attractor has forward attracting property.     

Properties of Neighborhoods of Attractors of Dynamical Systems

Mathematical Notes - The paper deals with the study of dynamical systems admitting compact attractors, which describe the behavior of trajectories of the system at infinity and play an important...     

Pullback Attractors of Nonautonomous and Stochastic Multivalued Dynamical Systems

In this paper we study the existence of pullback global attractors for multivalued processes generated by differential inclusions. First, we define multivalued dynamical processes, prove abstract results on the existence of -limit sets and global attractors, and study their topological properties (compactness, connectedness). Further, we apply the abstract results to nonautonomous differential inclusions of the reaction–diffusion type in which the forcing term can grow polynomially in time, and to stochastic differential inclusions as well.     

Attractors of Weakly Asymptotically Compact Set-Valued Dynamical Systems

The existence of weak attractors is established for set-valued dynamical systems which are weakly asymptotically compact and weakly dissipative. Here weak properties mean with respect to at least one trajectory for each initial value. A condition ensuring the uniqueness of such weak attractors is given. The results are illustrated with an application involving a partial differential inclusion in bounded and unbounded domains. Mathematics Subject Classifications (2000) 34D45, 37B25, 37B75, 58C06.     

Pullback Attractors for a 3D Non-autonomous Navier-Stokes-Voight Equations

Acta Mathematicae Applicatae Sinica, English Series - This paper is concerned with the existence of pullback attractors for the three dimensional non-autonomous Navier-Stokes-Voight equations for...     

定义在迭代函数系统吸引子上的动力系统的平衡态

在该文中, 令E表示一个迭代函数系统(X,T₁,…, T_m). 的吸引子. 定义连续自映射 f : E→E为f(x)=T^-1_j(x), x∈ T_j(E), j=1, …, m . 给定Given ψ ∈C_R(E), 令 K_ψ(δ, n = sup{∣∑^n-1_k=0[ψ(f ^kx)-ψ(f ^ky)]|:y ∈ B_x (δ, n)}, 这里B_x(δ, n) 表示Bowen球. 取一个扩张常数 ε, 记K_ψ=sup_n K_ψ(ε, n) , 定义ν(E)={ψ : K_ψ < ∞}. 对f : E → E, 作为Ruelle的一个定理^{[3, 定理2.1]}的一个应用, 我们证明每个ψ ∈ν(E)具有惟一的平衡态. 此结果推广了文献[12]中的主要结果.     

一类非线性非自治可伸缩板方程的一致吸引子

讨论了一类带有初值条件和固定边界条件的非线性非自治可伸缩板方程u_(tt)+△~2u+αu-△u_(tt)-M(||▽u||~2)△u-γ△u_t+f(u)=σ(x,t)证明了该系统的整体适定性.进一步研究了该系统的长时间动力学,利用建立整体弱解所生成的半过程一致渐近紧性,得到了有界区域Ω■R~n(n≥1)或无界开集中一致吸引子的存在性.     

Lyapunov Functions in Dimension Estimates of Attractors of Dynamical Systems

We discuss relations between the Lyapunov dimension and the topological, Hausdorff, and fractal dimensions of attractors. For the Henon and Lorenz systems, explicit formulas characterizing the Lyapunov dimension of their attractors are obtained. Bibliography: 23 titles.     

A Numerical Method for Establishing Liapunov Stability of Linear Second Order Non-autonomous Dynamical Systems

A numerical method which basically utilizes the Liapunov DirectMethod is presented which establishes sufficient conditionsfor the stability of the null solution of the nonautonomousdifferential equation x+b(t)x+a(t)x = 0. This is accomplishedwithout the unstructured task of searching for given Liapunovfunctions for the particular problem being analysed. The methodis simple and straightforward to apply, and can be used to obtainstability results as long as b is not identically zero. Thenumerical approach is demonstrated by applying it to the dampedMathieu equation, the Euler equation, and an equation with quasiperiodiccoefficients.     

Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Reaction-diffusion Equations

This paper dealswith non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s ∈ (0,1). We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.     

关于非自治Benjiamin-Bona-Mohony方程拉回吸引子的一个注记(英文）

In this paper,we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.     

非自治Plate方程时间依赖强拉回吸引子的存在性

结合Plinio等人([Plinio D,Duane G S,Temarn R,Time-dependent attractor for the oscillon equation,Discrete Contin Dyn Syst,2011,29(1):141-167.])提出的时间依赖全局吸引子概念,运用压缩函数的方法,证明了带有时间依赖系数的非自治Plate方程时间依赖拉回吸引子在空间H~4(Ω)∩H~2_0(Ω)×H~2_0(Ω)中的存在性.     

Equi-Attraction and Continuous Dependence of Strong Attractors of Set-Valued Dynamical Systems on Parameters

Equi-attraction properties of the global attractors of a family of set-valued dynamical systems {G_λ, λ∈Λ} with respect to a parameter λ∈Λ, where Λ is a compact metric space, are investigated. In particular, under appropriate conditions, it is shown that the equi-attraction of the family is equivalent to the continuity of in λ with respect to the Hausdorff distance. An example involving differential inclusions is given. Mathematics Subject Classifications (2000) Primary 47H17, 58F03, 34C20. Desheng Li: Supported by NNSF of China (10251002) and NNSF of Gansu province (3ZS041-A25-006).     

一类非自治时滞非局部模型的一致吸引子

本文研究了一类具有非局部反应项的非自治时滞偏微分方程的长时间性态,利用平移紧函数的性质,将相空间扩展使得非自治系统生成的过程提升为半群,再利用半群理论证明了一致吸引子的存在性.     

Relation between Different Types of Global Attractors of Set-Valued Nonautonomous Dynamical Systems

The article is devoted to the study of the relation between forward and pullback attractors of set-valued nonautonomous dynamical systems (cocycles). Here it is proved that every compact global forward attractor is also a pullback attractor of the set-valued nonautonomous dynamical system. The inverse statement, generally speaking, is not true, but we prove that every global pullback attractor of an α-condensing set-valued cocycle is always a local forward attractor. The obtained general results are applied while studying periodic and homogeneous systems. We give also a new criterion of the absolute asymptotic stability of nonstationary discrete linear inclusions. Dedicated to our friend Professor Enrico Primo Tomasini on the occasion of his 55th birthdayMathematics Subject Classifications (2000) Primary: 34C35, 34D20, 34D40, 34D45, 58F10,58F12, 58F39; secondary: 35B35, 35B40.     

Global Attractors for Multivalued Random Dynamical Systems Generated by Random Differential Inclusions with Multiplicative Noise

In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.     

Robustness of Random Attractors for a Stochastic Reaction-Diffusion System

Asymptotic pullback dynamics of a typical stochastic reaction-diffusion system, the reversible Schnackenberg equations, with multiplicative white noise is investigated. The robustness of random attractor with respect to the reverse reaction rate as it tends to zero is proved through the uniform pullback absorbing property and the uniform convergence of reversible to non-reversible cocycles. This result means that, even if the reverse reactions would be neglected, the dynamics of this class of stochastic reversible reaction-diffusion systems can still be captured by the random attractor of the non-reversible stochastic raction-diffusion system in a long run.