共查询到20条相似文献,搜索用时 31 毫秒
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Jos M.R. Sanjurjo 《Journal of Differential Equations》2007,243(2):238-255
We study the homotopical and homological properties of the attractors evolving from a generalized Hopf bifurcation. We consider the Lorenz equations for parameter values near the Hopf bifurcation and study a natural Morse decomposition of the global attractor, calculating the Čech homotopy type of the Lorenz attractor, the shape indexes of the Morse sets and the Morse equation of the decomposition. 相似文献
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Tamara Fastovska 《Mathematical Methods in the Applied Sciences》2016,39(13):3669-3690
We consider a nonlinear system of thermoelasticity in shape memory alloys without viscosity. The existence and uniqueness of strong and weak solutions and the existence of a compact global attractor in an appropriate space are proved. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(3):1501-1508
This paper has investigated the localization problem of compact invariant sets of a new chaotic system with the help of the iteration theorem and the first order extremum theorem. If there are more iterations, then the estimation for the bound of the system will be more accurate, because the shape of the chaotic attractor is irregular. We establish that all compact invariant sets of this system are located in the intersection of a ball with two frusta and we also compute its parameters. It is a great advantage that we can attain a smaller bound of the chaotic attractor compared with the classical method. One numerical example illustrating a localization of a chaotic attractor is presented as well. 相似文献
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Morgan Pierre 《Numerical Functional Analysis & Optimization》2013,34(16):1755-1784
AbstractWe consider a space semidiscretization of the Allen–Cahn equation by continuous piecewise linear finite elements. For every mesh parameter h, we build an exponential attractor of the dynamical system associated with the approximate equations. We prove that, as h tends to 0, this attractor converges for the symmetric Hausdorff distance to an exponential attractor of the dynamical system associated with the Allen–Cahn equation. We also prove that the fractal dimension of the exponential attractor and of the global attractor is bounded by a constant independent of h. Our proof is adapted from the result of Efendiev, Miranville and Zelik concerning the continuity of exponential attractors under perturbation of the underlying semigroup. Here, the perturbation is a space discretization. The case of a time semidiscretization has been analyzed in a previous paper. 相似文献
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M. Scheutzow 《Archiv der Mathematik》2002,78(3):233-240
Several non-equivalent definitions of an attractor of a random dynamical system have been proposed in the literature. We consider a rather simple special case: random dynamical systems with state space [0, ¥) [0, \infty) which fix 0. We examine conditions under which the set {0} is an attractor for three different notions of an attractor. It turns out that even in this simple case the various concepts are quite different. The purpose of this note is to highlight these differences and thus provide a basis for discussion about the "correct" concept of a random attractor. 相似文献
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A. Giraldo 《Topology and its Applications》2011,158(2):167-176
In this paper we consider two notions of attractors for semidynamical systems defined in metric spaces. We show that Borsuk's weak and strong shape theories are a convenient framework to study the global properties which the attractor inherits from the phase space.Moreover we obtain pointed equivalences (even in the absence of equilibria) which allow to consider also pointed invariants, like shape groups. 相似文献
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Yu. Ilyashenko 《Regular and Chaotic Dynamics》2010,15(2-3):328-334
A diffeomorphism is said to have a thick attractor provided that its Milnor attractor has positive but not full Lebesgue measure. We prove that there exists an open set in the space of boundary preserving step skew products with a fiber [0,1], such that any map in this set has a thick attractor. 相似文献
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In this paper, we study the primary instability of the damped Kuramoto–Sivashinsky equation under a periodic boundary condition. We prove that it bifurcates from the trivial solution to an attractor which determines the long time dynamics of the system. Using the attractor bifurcation theorem and the center manifold theory, we describe the bifurcated attractor in detail. 相似文献
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Hongyan Li Shengfan Zhou 《Communications in Nonlinear Science & Numerical Simulation》2012,17(9):3579-3586
In this paper, we study the long-time behavior of solutions for a non-autonomous strongly damped wave equation. We first prove the existence of a uniform attractor for the equation with a translation compact driving force and then obtain an upper estimate for the Kolmogorov ε-entropy of the uniform attractor. Finally we obtain an upper bound of the fractal dimension of the uniform attractor with quasiperiodic force. 相似文献
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Abstract
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is
fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining
part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under
the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global
attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence
of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the
non-autonomous case by the limiting global attractor.
* Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”. 相似文献
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We construct an exponential attractor for a second order lattice dynamical system with nonlinear damping arising from spatial discretization of wave equations in Rk. And we obtain fractal dimension of the exponential attractor and its finite-dimensional approximation. 相似文献
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We study the boundary value problem for the equations of motion of incompressible viscoelastic medium with an objective constitutive law of Jeffreys kind. We show existence of global weak solutions for any initial data and construct their minimal uniform trajectory attractor and uniform global attractor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Guided by classical concepts, we define the notion of ends of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points are then linked to idempotent maps. A commutative diagram illustrates the natural relationships between the infinite walks in a semigroup and components of an attractor in more detail. We show in particular that, if an iterated function system is one-ended, the associated attractor is connected, and ask whether every connected attractor (fractal) conversely admits a one-ended system. 相似文献
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Sakineh Habibi 《Mathematica Slovaca》2014,64(5):1237-1248
We study the long time behavior of delay differential equation, considered in a bounded domain in ? d . Using the short trajectory method to prove the existence of the exponential attractor. Also we have estimates on the fractal dimension of an exponential attractor. 相似文献
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Pedro Marín-Rubio José Real 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3956-3963
For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier-Stokes model, improving some previous results on attractor theory. 相似文献
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We construct an exponential attractor for semigroup in Banach space by using ω-limit compactness method and provide a new method to prove the existence of an exponential attractor in uniformly convex Banach space. As a simple application, we prove the existence of an exponential attractor for reaction diffusion equations. 相似文献
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Mihail and Miculescu introduced the notion of a generalized iterated function system (GIFS in short), and proved that every GIFS generates an attractor. (In our previous paper we gave this notion a more general setting.) In this paper we show that for any m≥2, there exists a Cantor subset of the plane which is an attractor of some GIFS of order m , but is not an attractor of a GIFS of order m−1. In particular, this result shows that there is a subset of the plane which is an attractor of some GIFS, but is not an attractor of an IFS. We also give an example of a Cantor set which is not an attractor of a GIFS. 相似文献
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Alain Miranville 《Applications of Mathematics》2003,48(1):31-47
In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua. 相似文献