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71.
This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces. 相似文献
72.
We study the attractors of a finite system of planar contraction similarities S
j
(j=1,...,n) satisfying the coupling condition: for a set {x
0,...,x
n} of points and a binary vector (s
1,...,s
n
), called the signature, the mapping S
j
takes the pair {x
0,x
n} either into the pair {x
j-1,x
j
} (if s
j
=0) or into the pair {x
j
, x
j-1} (if s
j
=1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis. 相似文献
73.
Oliver M. Tearne 《Probability Theory and Related Fields》2008,141(1-2):1-18
This paper concerns comparisons between attractors for random dynamical systems and their corresponding noiseless systems.
It is shown that if a random dynamical system has negative time trajectories that are transient or explode with probability
one, then the random attractor cannot contain any open set. The result applies to any Polish space and when applied to autonomous
stochastic differential equations with additive noise requires only a mild dissipation of the drift. Additionally, following
observations from numerical simulations in a previous paper, analytical results are presented proving that the random global
attractors for a class of gradient-like stochastic differential equations consist of a single random point. Comparison with
the noiseless system reveals that arbitrarily small non-degenerate additive white noise causes the deterministic global attractor,
which may have non-zero dimension, to ‘collapse’. Unlike existing results of this type, no order preserving property is necessary.
相似文献
74.
Summary. The dynamical behavior of the damped sine-Gordon equation with homogeneous Neumann boundary condition is studied. It is shown
that the equation has an unbounded one-dimensional global attractor in a suitable functional space when the ``damping' and
the ``diffusing' are not very small.
Received March 16, 1999; accepted December 10, 1999 相似文献
75.
Yu. S. Kolesov 《Mathematical Notes》1997,62(5):623-628
For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997.
Translated by O. V. Sipacheva 相似文献
76.
本文考虑Hopfield型模型的收敛性问题和吸引子的吸引域的刻画。证明了N<+∞与N=+∞时Hopfield模型在几乎处处的意义下收敛于吸引集。当N<+∞时,模型将在有限时间内稳定于某一吸引子上.对于N<+∞与N=+ ∞的情形,分别得到了吸引域的一个集的刻画。 相似文献
77.
非光滑区域上非自治Navier-Stokes 方程非齐边界问题的吸引子 总被引:1,自引:0,他引:1
本文研究在2维Lipschitz区域上Navier-Stokes方程的非齐边界问题的长时间行为,在外力是时间的拟周期下,通过引入双参过程的概念,证明一致吸引子A的存在性,并给出一致吸引子A的Hausdorff维数的上界估计。 相似文献
78.
Tomá s Caraballo Hans Crauel José A. Langa James C. Robinson 《Proceedings of the American Mathematical Society》2007,135(2):373-382
We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, , by noise. While a single multiplicative Itô noise of sufficient intensity will stabilise the origin, its Stratonovich counterpart leaves the dimension of the attractor essentially unchanged. We then show that a collection of multiplicative Stratonovich terms can make the origin exponentially stable, while an additive noise of sufficient richness reduces the random attractor to a single point.
79.
We present the results of the nonlinear analysis of a near-wall turbulence signal, measured using a Laser Doppler Anemometer.
Despite being preliminary in part, the results highlight some interesting aspects of the dynamics of coherent structures.
Careful reconstruction of the dynamics from the scalar time series highlight particular phases of the bursting cycle, corresponding
to the VITA detections, immersed in the overall high-dimension dynamics: the possibility to distinguish these trajectories
in the embedding space provides indications for conditional sampling techniques on the reconstructed attractor. The application
of nonlinear prediction to a system of high-dimension produces forecasts of rapidly decreasing quality over time, with no
consequences for practical applications. Much more interesting instead is the analysis of the forecast errors for very short
forecast intervals, where we observed a greater difficulty to predict the beginning of coherent structure instability probably
due to the quasi-random forcing of the outer flow. 相似文献
80.
This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation. Furthermore, the existence of exponential attractors is also derived. 相似文献