Results 321 to 330 of about 4,970,219 (372)

Nonstandard analysis of global attractors

Mathematical Logic Quarterly, 2015
Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness.
Dalibor Pražák, Jakub Slavík
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The Existence of a Global Attractor for the Forced Critical Surface Quasi-Geostrophic Equation in $$L^2$$L2

, 2014
We prove that the critical surface quasi-geostrophic equation driven by a force f possesses a compact global attractor in $$L^2(\mathbb T^2)$$L2(T2) provided $$f\in L^p(\mathbb T^2)$$f∈Lp(T2) for some $$p>2$$p>2.
A. Cheskidov, Mimi Dai
semanticscholar   +1 more source

Global attractor alphabet of neural firing modes.

Journal of Neurophysiology, 2013
The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold ...
Y. Baram
semanticscholar   +1 more source

Global Attractors and a Lubrication Problem

2016
We start this chapter from necessary background on the theory of fractal dimension. Next, we formulate and study a problem which models the two-dimensional boundary driven shear flow in lubrication theory. After the derivation of the energy dissipation rate estimate and a version of Lieb–Thirring inequality we provide an estimate from above on the ...
Grzegorz Łukaszewicz, Piotr Kalita
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Global attractors and approximate inertial

Applicable Analysis, 1993
An abstract nonautonomous differential equation, u' + Au + F(u) = f ( t ) , is considered using assumptions appropriate for systems of reaction-diffusion equations on multi-dimensional spatial domains. A priori estimates establish the existence of absorbing balls in relevant function spaces, and nonsequently the existence of a global attractor is ...
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Global attractors and bifurcations

1996
We present some recent developments in the study of attractors of smooth dynamical systems, specially attractors whose basin has a global character. A key point in our approach is to explore the relations between this study and that of main bifurcation mechanisms.
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Global attractors for a vegetation model

Asymptotic Analysis, 2011
In this article, a rigorous mathematical treatment of the dryland vegetation model introduced by Gilad et al. [Phys. Rev. Lett. 98(9) (2004), 098105-1–098105-4, J. Theoret. Biol. 244 (2007), 680–691] is presented. We prove the existence and uniqueness of solutions in (L1(Ω))3 and the existence of global attractors in L1(Ω;𝒟), where 𝒟 is an invariant ...
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Consequences Regarding the Global Attractor

1989
Let X be the global attractor of the dissipative system under consideration. Recall that X is the largest set in H with the properties (i) S(t)X = X for t ≥ 0, (ii) X is bounded in H, (iii) dist(S(t)uo,X) → 0 as t → ∞ for all uo ∈ H.
B. Nicolaenko, Ciprian Foias, Peter Constantin, R. Teman   +3 more
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Unstable Sets of Periodic Orbits and the Global Attractor for Delayed Feedback

, 2012
The differential equation ẋ(t) = −μx(t) + f(x(t − 1)) with μ > 0 and a C-smooth real function f satisfying f(0) = 0 and f ′ > 0 models a system with instantaneous friction and delayed feedback.
T. Krisztin
semanticscholar   +1 more source

Nontrivial Global Attractors in 2-D Multistable Attractor Neural Networks

IEEE Transactions on Neural Networks, 2009
Attractor dynamics is a crucial problem for attractor neural networks, as it is the underling computational mechanism for memory storage and retrieval in neural systems. This brief studies a class of attractor network consisting of linearized threshold neurons, and analyzes global attractors based on a parameterized 2-D model.
Weinian Zhang, Lan Zou, Huajin Tang, Kay Chen Tan   +3 more
openaire   +3 more sources