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Globally and locally attractive solutions for quasi-periodic ally forced systems

Bartuccelli, Michele, Deane, Jonathan and Gentile, G (2007) Globally and locally attractive solutions for quasi-periodic ally forced systems JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 328 (1). pp. 699-714.

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Abstract

We consider a class of differential equations, x¨ + γ x˙ + g(x) = f (ωt), with ω ∈ Rd , describing onedimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x) = x2p+1, p ∈ N, we show that, when the dissipation coefficient is large enough, there is only one such trajectory and that it describes a global attractor. In the case of more general nonlinearities, including g(x) = x2 (describing the varactor equation), we find that there is at least one trajectory which describes a local attractor.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Bartuccelli, MicheleM.Bartuccelli@surrey.ac.ukUNSPECIFIED
Deane, JonathanJ.Deane@surrey.ac.ukUNSPECIFIED
Gentile, GUNSPECIFIEDUNSPECIFIED
Date : 1 April 2007
Identification Number : 10.1016/j.jmaa.2006.05.055
Copyright Disclaimer : © 2007. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords : Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, MATHEMATICS, MATHEMATICS, APPLIED, dissipative systems, quasi-periodically forced systems, varactor equation, attractor, global attractivity, 2-LEVEL SYSTEMS, POTENTIALS, EQUATION
Related URLs :
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 07 Jul 2017 16:27
URI: http://epubs.surrey.ac.uk/id/eprint/1442

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