共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article, we introduce the notions of strong centers of attraction for multi-valued dynamical systems on arbitrary metric spaces. And we obtain strong centers of attraction for multi-valued dynamical systems. 相似文献
2.
Dynamics of systems on infinite lattices 总被引:1,自引:0,他引:1
Bixiang Wang 《Journal of Differential Equations》2006,221(1):224-245
The dynamics of infinite-dimensional lattice systems is studied. A necessary and sufficient condition for asymptotic compactness of lattice dynamical systems is introduced. It is shown that a lattice system has a global attractor if and only if it has a bounded absorbing set and is asymptotically null. As an application, it is proved that the lattice reaction-diffusion equation has a global attractor in a weighted l2 space, which is compact as well as contains traveling waves. The upper semicontinuity of global attractors is also obtained when the lattice reaction-diffusion equation is approached by finite-dimensional systems. 相似文献
3.
Ahmed Y. Abdallah 《Journal of Differential Equations》2011,251(6):1489-1504
In Abdallah (2008, 2009) [2] and [3], we have investigated the existence of exponential attractors for first and second order autonomous lattice dynamical systems. Within this work, in l2, we carefully study the existence of a uniform exponential attractor for the family of processes associated with an abstract family of first order non-autonomous lattice dynamical systems with quasiperiodic symbols acting on a closed bounded set. 相似文献
4.
We derive new necessary and sufficient conditions for admissibility
of observation operators for certain C
0-semigroups. We also prove a new
sufficient criterion for admissibility for observation operators with infinite-dimensional
output space on contraction semigroups. If the contraction semigroup
is completely non-unitary and its co-generator has finite defect indices,
then this criterion is also necessary. In the case of the right shift semigroup
on L
2(0,), these conditions translate into conditions for the boundedness
of Hankel operators. 相似文献
5.
6.
Lu Yang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(12):3876-3883
In this paper, we study the long-time behavior of the reaction-diffusion equation with dynamical boundary condition, where the nonlinear terms f and g satisfy the polynomial growth condition of arbitrary order. Some asymptotic regularity of the solution has been proved. As an application of the asymptotic regularity results, we can not only obtain the existence of a global attractor A in (H1(Ω)∩Lp(Ω))×Lq(Γ) immediately, but also can show further that A attracts every L2(Ω)×L2(Γ)-bounded subset with (H1(Ω)∩Lp+δ(Ω))×Lq+κ(Γ)-norm for any δ,κ∈[0,∞). 相似文献
7.
A. A. Kosov 《Journal of Applied and Industrial Mathematics》2010,4(2):200-212
We improve the available necessary conditions and sufficient conditions for the Dstability and additive D-stability of matrices. We define these dynamical properties with respect to a finite parallelepiped and propose an algorithm
for checking them. For a particular class of matrices called Svicobians, we obtain some constructive necessary and sufficient
conditions for Dstabilizability, D-stability, and additive D-stability. 相似文献
8.
In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh
–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper. 相似文献
9.
José F. Alves Jorge M. Freitas Stefano Luzzatto Sandro Vaienti 《Advances in Mathematics》2011,(2):1203
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of correlations. Such geometric structures are generally highly non-trivial and thus a natural question is the extent to which this approach can be applied. In this paper we show that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration. As a by product of our techniques we also obtain some new results on large deviations for certain classes of systems which include Viana maps and multidimensional piecewise expanding maps. 相似文献
10.
Peter Giesl 《Journal of Approximation Theory》2008,153(2):184-211
The basin of attraction of an asymptotically stable fixed point of the discrete dynamical system given by the iteration xn+1=g(xn) can be determined through sublevel sets of a Lyapunov function. In Giesl [On the determination of the basin of attraction of discrete dynamical systems. J. Difference Equ. Appl. 13(6) (2007) 523–546] a Lyapunov function is constructed by approximating the solution of a difference equation using radial basis functions. However, the resulting Lyapunov function is non-local, i.e. it has no negative discrete orbital derivative in a neighborhood of the fixed point. In this paper we modify the construction method by using the Taylor polynomial and thus obtain a Lyapunov function with negative discrete orbital derivative both locally and globally. 相似文献
11.
Yang Lu 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4012-4025
In this paper, we first introduce the concept of a closed process in a Banach space, and we obtain the structure of a uniform attractor of the closed process by constructing a skew product-flow on the extended phase space. Then, the properties of the kernel section of closed process are investigated. Moreover, we prove the existence and structure of the uniform attractor for the reaction-diffusion equation with a dynamical boundary condition in Lp without any restriction on the growth order of the nonlinear term. 相似文献
12.
The paper is concerned with the question of smoothness of the carrying simplex S for a discrete-time dissipative competitive dynamical system. We give a necessary and sufficient criterion for S being a C1 submanifold-with-corners neatly embedded in the nonnegative orthant, formulated in terms of inequalities between Lyapunov exponents for ergodic measures supported on the boundary of the orthant. This completes one thread of investigation occasioned by a question posed by M.W. Hirsch in 1988. Besides, amenable conditions are presented to guarantee the Cr (r?1) smoothness of S in the time-periodic competitive Kolmogorov systems of ODEs. Examples are also presented, one in which S is of class C1 but not neatly embedded, the other in which S is not of class C1. 相似文献
13.
For systems of functional differential equations with nonlinear deviation of argument, we obtain sufficient conditions for the existence of families of their solutions that are continuously differentiable for t R
+. We also investigate the asymptotic behavior of these solutions. 相似文献
14.
Barbara Przebieracz 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1980-1988
In this paper we prove the stability of the functional equation F(s,F(t,x))=F(s+t,x) in the class of functions F:R×I→I, which are continuous with respect to each variable, and where I⊂R is a real interval. We also discuss the stability in the sense of Hyers-Ulam of dynamical systems on I. We show some properties of δ-approximate solutions of the translation equation on a real interval. 相似文献
15.
《Quaestiones Mathematicae》2013,36(4):475-477
Abstract Using the notion of a spectral set introduced by von-Neumann, we give some characterizations of C+ -algebras. Two conditions, each of which is necessary and sufficient for a Banach algebra to be uniform, are also obtained. 相似文献
16.
For the unilateral shift operator U on the Hardy space H2(T), we describe conditions on operators T, acting on H2(T), that are necessary and sufficient for the pair (U, T) to be jointly hyponormal. One necessary condition is that T be a Toeplitz operator. Consequently, we study certain nonanalytic symbols that give rise to Toeplitz operators hyponormal with the shift, and thereby obtain examples of noncommuting, jointly hyponormal pairs.Supported in part by a research grant from NSERC 相似文献
17.
In this paper we discuss the properties of the Schwarzian derivative, integral means and the affine and linear invariant families of biharmonic mappings. First, we introduce the Schwarzian derivative S(F) for biharmonic mappings F = ∣z∣2G + H, and obtain several necessary and sufficient conditions for S(F) to be analytic. Second, we introduce the subordination of biharmonic mappings and obtain inequalities for integral means of subordinate biharmonic mappings. Finally, we introduce the affine and linear invariant families of biharmonic mappings and prove several estimates related to the Jacobian of functions in these invariant families. 相似文献
18.
Pitambar Das 《Proceedings Mathematical Sciences》1993,103(3):341-347
In this paper, we obtain the sufficient and necessary conditions for all solutions of the odd-order nonlinear delay differential equation.x (n)+Q(t)f(x(g(t)))=0 to be oscillatory. In particular, ifn=1, Q(t)>0, f(x)=x α, where α∈(0,1) and is a ratio of odd integers andg(t)=t?? for some ?>0, then every solution of (*) oscillates if and only if ∫∞Q(s)ds=∞. 相似文献
19.
Jian Li 《Topology and its Applications》2011,158(16):2221-2231
Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z+ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z+:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ?(Fwt)-transitive if and only if it is weakly disjoint from every P-system. 相似文献
20.
Feng Qi Senlin Guo Bai-Ni Guo 《Journal of Computational and Applied Mathematics》2010,233(9):2149-331
In the present paper, we establish necessary and sufficient conditions for the functions xα|ψ(i)(x+β)| and α|ψ(i)(x+β)|−x|ψ(i+1)(x+β)| respectively to be monotonic and completely monotonic on (0,∞), where i∈N, α>0 and β≥0 are scalars, and ψ(i)(x) are polygamma functions. 相似文献