Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations


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
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/68368
Official URL:https://doi.org/10.1007/s00332-009-9045-2
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