Globally and locally attractive solutions for quasi-periodically forced systems |
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Authors: | Michele V. Bartuccelli |
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Affiliation: | a Department of Mathematics and Statistics, University of Surrey, Guildford, GU2 7XH, UK b Dipartimento di Matematica, Università di Roma Tre, Roma I-00146, Italy |
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Abstract: | We consider a class of differential equations, , with ω∈Rd, describing one-dimensional 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. |
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Keywords: | Dissipative systems Quasi-periodically forced systems Varactor equation Attractor Global attractivity |
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