Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations

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Bakri, Taoufik and Meijer, Hil G.E. and Verhulst, Ferdinand (2009) Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations. Journal of Nonlinear Science, 19 (5). pp. 571-596. ISSN 0938-8974

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Abstract:Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited wave equation. We find fast dynamics in a finite, resonant part of the spectrum and slow dynamics elsewhere. The resonant part corresponds with an almost-invariant manifold and displays bifurcations into a wide variety of phenomena among which are 2- and 3-tori.
Item Type:Article
Copyright:© 2009 Springer
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/68368
Official URL:http://dx.doi.org/10.1007/s00332-009-9045-2
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