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Global Attraction to Solitary Waves
 in Models Based on the KleinGordon Equation, Symmetry, Integrability and Geometry: Methods and Applications 4
, 2008
"... We review recent results on global attractors of U(1)invariant dispersive Hamiltonian systems. We study several models built upon the KleinGordon equation and sketch the proof that in these models, under certain generic assumptions, the weak global attractor is represented by the variety of all so ..."
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We review recent results on global attractors of U(1)invariant dispersive Hamiltonian systems. We study several models built upon the KleinGordon equation and sketch the proof that in these models, under certain generic assumptions, the weak global attractor is represented by the variety of all
Global Attractivity in a Competition System with Feedback Cdntrols
, 2000
"... AbstractSufficient conditions are derived for the existence of a globally attracting positive equilibrium of a two species competition system with feedback controls; the indirect controls can act instantaneously or with a fixed discrete delay. @ 2003 Elsevier Science Ltd. All rights reserved. Keywo ..."
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AbstractSufficient conditions are derived for the existence of a globally attracting positive equilibrium of a two species competition system with feedback controls; the indirect controls can act instantaneously or with a fixed discrete delay. @ 2003 Elsevier Science Ltd. All rights reserved
Globally attractive and positive invariant set of the Lorenz system
 Internat
"... In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system satisfie ..."
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Cited by 4 (3 self)
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In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system
On global attractivity of solutions of a functionalintegral equation
"... We prove an existence theorem for a quadratic functionalintegral equation of mixed type. The functionalintegral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functi ..."
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that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [0, ∞) and those solutions are globally attractive. Key words and phrases: Functionalintegral equation, existence, global attractivity, measure of noncompactness, fixed point theorem due to Darbo.
Planar Embeddings with a Globally Attracting Fixed Point
, 2007
"... We consider sufficient conditions which guarantee that an embedding from the plane R 2 into itself has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding. 1 ..."
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Cited by 8 (1 self)
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We consider sufficient conditions which guarantee that an embedding from the plane R 2 into itself has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding. 1
Global Attractivity of a Rational Difference Equation
"... Abstract: In this paper, we investigate the global attractivity of positive solutions of the nonlinear difference equation xn+1 = ax3 n+ bxnx2 n−1 + cx2 nxn−1+ dx3 n−1 Ax3 n+ Bxnx2 n−1 +Cx2 nxn−1+ Dx3, n=0,1,... n−1 where the parameters a, b, c, d, A, B, C, D are positive real numbers and the initia ..."
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Abstract: In this paper, we investigate the global attractivity of positive solutions of the nonlinear difference equation xn+1 = ax3 n+ bxnx2 n−1 + cx2 nxn−1+ dx3 n−1 Ax3 n+ Bxnx2 n−1 +Cx2 nxn−1+ Dx3, n=0,1,... n−1 where the parameters a, b, c, d, A, B, C, D are positive real numbers
Virtual Time and Global States of Distributed Systems
 PARALLEL AND DISTRIBUTED ALGORITHMS
, 1988
"... A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a consiste ..."
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Cited by 741 (6 self)
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A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a
A Global Attracting Set for the KuramotoSivashinsky Equation
 Comm. Math. Phys
, 1993
"... this paper, we prove new bounds on the KuramotoSivashinsky equation (KS) by extending the ingenious method of Nicolaenko, Scheurer, and Temam [NST]. We study the KSequation in its "derivative form:" ..."
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Cited by 45 (1 self)
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this paper, we prove new bounds on the KuramotoSivashinsky equation (KS) by extending the ingenious method of Nicolaenko, Scheurer, and Temam [NST]. We study the KSequation in its "derivative form:"
The global attractivity of the rational difference equation yn =1
 yn−k , Proc.Amer.Math.Soc., 135 (2007), 1133–1140. MR2262916 yn−m (2007f:39006
"... Abstract. This paper studies the behavior of positive solutions of the recursive equation yn =1+ yn−k, n =0, 1, 2,..., yn−m with y−s,y−s+1,...,y−1 ∈ (0, ∞) and k, m ∈ {1, 2, 3, 4,...}, where s = max{k, m}. We prove that if gcd(k, m) = 1, with k odd, then yn tends to 2, exponentially. When combined ..."
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Cited by 27 (8 self)
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with a recent result of E. A. Grove and G. Ladas (Periodicities in Nonlinear Difference Equations, Chapman & Hall/CRC Press, Boca Raton (2004)), this answers the question when y =2 is a global attractor. 1.
A fast iterative shrinkagethresholding algorithm with application to . . .
, 2009
"... We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterat ..."
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Cited by 1055 (8 self)
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We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast
Results 1  10
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