The Experts below are selected from a list of 747 Experts worldwide ranked by ideXlab platform
Elena Panteley - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic phase synchronization of Kuramoto model with weighted non-symetric interconnections: A case study
2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single Purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
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CDC - Asymptotic phase synchronization of Kuramoto model with weighted non-symmetric interconnections: A case study
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single Purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
Elias Jarlebring - One of the best experts on this subject based on the ideXlab platform.
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Critical delays and polynomial Eigenvalue problems
Journal of Computational and Applied Mathematics, 2009Co-Authors: Elias JarlebringAbstract:In this work we present a new method to compute the delays of delay-differential equations (DDEs), such that the DDE has a Purely Imaginary Eigenvalue. For delay-differential equations with multiple delays, the critical curves or critical surfaces in delay space (that is, the set of delays where the DDE has a Purely Imaginary Eigenvalue) are parameterized. We show how the method is related to other works in the field by treating the case where the delays are integer multiples of some delay value, i.e., commensurate delays. The parameterization is done by solving a quadratic Eigenvalue problem which is constructed from the vectorization of a matrix equation and hence typically of large size. For commensurate delay-differential equations, the corresponding equation is a polynomial Eigenvalue problem. As a special case of the proposed method, we find a closed form for a parameterization of the critical surface for the scalar case. We provide several examples with visualizations where the computation is done with some exploitation of the structure of Eigenvalue problems.
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On critical delays for linear neutral delay systems
2007 European Control Conference (ECC), 2007Co-Authors: Elias JarlebringAbstract:In this work we address the problem of finding the critical delays of a linear neutral delay system, i.e., the delays such that the system has a Purely Imaginary Eigenvalue. Even though neutral delay systems exhibit some discontinuity properties with respect to changes in the delays an essential part in a non-conservative stability analysis with respect to changes in the delays, is the computation of the critical delays.
Ali El Ati - One of the best experts on this subject based on the ideXlab platform.
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Asymptotic phase synchronization of Kuramoto model with weighted non-symetric interconnections: A case study
2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single Purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
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CDC - Asymptotic phase synchronization of Kuramoto model with weighted non-symmetric interconnections: A case study
52nd IEEE Conference on Decision and Control, 2013Co-Authors: Ali El Ati, Elena PanteleyAbstract:We consider a synchronization problem for the Kuramoto oscillators using a linear modeling framework. For the general case of Kuramoto model with directed and weighted graph of interconnections we show that the problem of existence of phase locked solutions is equivalent to an algebraic problem of existence of a corresponding matrix with a single Purely Imaginary Eigenvalue. In the case of complete input- output weighted graphs this approach allows to give analytical expressions both for the synchronization frequencies and the phase locked solutions and, on the next step, to analyze their stability properties.
Alastair Spence - One of the best experts on this subject based on the ideXlab platform.
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Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems
SIAM Journal on Matrix Analysis and Applications, 2010Co-Authors: Karl Meerbergen, Alastair SpenceAbstract:The detection of a Hopf bifurcation in a large-scale dynamical system that depends on a physical parameter often consists of computing the right-most Eigenvalues of a sequence of large sparse Eigenvalue problems. Guckenheimer, Gueron, and Harris-Warrick [SIAM J. Numer. Anal., 34 (1997), pp. 1-21] proposed a method that computes a value of the parameter that corresponds to a Hopf point without actually computing right-most Eigenvalues. This method utilizes a certain sum of Kronecker products and involves the solution of matrices of squared dimension, which is impractical for large-scale applications. However, if good starting guesses are available for the parameter and the Purely Imaginary Eigenvalue at the Hopf point, then efficient algorithms are available. In this paper, we propose a method for obtaining such good starting guesses, based on finding Purely Imaginary Eigenvalues of a two-parameter Eigenvalue problem (possibly arising after a linearization process). The problem is formulated as an inexact inverse iteration method that requires the solution of a sequence of Lyapunov equations with low rank right-hand sides. It is this last fact that makes the method feasible for large systems. The power of our method is tested on four numerical examples.
Pei-kee Lin - One of the best experts on this subject based on the ideXlab platform.
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Extremal properties of contraction semigroups onc _0
Semigroup Forum, 1996Co-Authors: Pei-kee LinAbstract:For any complex Banach space X , let J denote the duality mapping of X . For any unit vector x in X and any ( C _0) contraction semigroup ( T _ t )_ t >0 on X , Baillon and Guerre-Delabriere proved that if X is a smooth reflexive Banach space and if there is x ^*∈ J(x) such that ÷〈( T(t)x, J(x)〈 ÷→1 as t →∞, then there is a unit vector y ∈ X which is an eigenvector of the generator A of ( T _ t )_ t >0 associated with a Purely Imaginary Eigenvalue. They asked whether this result is still true if X is replaced by c _0. In this article, we show the answer is negative
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Extremal properties of contraction semigroups on c 0
Semigroup Forum, 1996Co-Authors: Pei-kee LinAbstract:For any complex Banach spaceX, letJ denote the duality mapping ofX. For any unit vectorx inX and any (C 0) contraction semigroup (T t ) t>0 onX, Baillon and Guerre-Delabriere proved that ifX is a smooth reflexive Banach space and if there isx *∈J(x) such that ÷〈(T(t)x, J(x)〈÷→1 ast→∞, then there is a unit vectory∈X which is an eigenvector of the generatorA of (T t ) t>0 associated with a Purely Imaginary Eigenvalue. They asked whether this result is still true ifX is replaced byc 0. In this article, we show the answer is negative
